I have a Rounded Border that contains a ComboBox
Check your Previous Posts asking the same
Unable to style WPF ComboBox on Mouse Hover
How to change ComboBox's Background Property during Mouse Hover
EDIT
Use like this. Below is the default controltemplate of the combobox. Note the commented line of code for your requirement
<Window.Resources>
<!-- Fill Brushes -->
<LinearGradientBrush x:Key="NormalBrush" StartPoint="0,0" EndPoint="0,1">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#FFF" Offset="0.0"/>
<GradientStop Color="#CCC" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<LinearGradientBrush x:Key="HorizontalNormalBrush" StartPoint="0,0" EndPoint="1,0">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#FFF" Offset="0.0"/>
<GradientStop Color="#CCC" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<LinearGradientBrush x:Key="LightBrush" StartPoint="0,0" EndPoint="0,1">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#FFF" Offset="0.0"/>
<GradientStop Color="#EEE" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<LinearGradientBrush x:Key="HorizontalLightBrush" StartPoint="0,0" EndPoint="1,0">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#FFF" Offset="0.0"/>
<GradientStop Color="#EEE" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<LinearGradientBrush x:Key="DarkBrush" StartPoint="0,0" EndPoint="0,1">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#FFF" Offset="0.0"/>
<GradientStop Color="#AAA" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<LinearGradientBrush x:Key="PressedBrush" StartPoint="0,0" EndPoint="0,1">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#BBB" Offset="0.0"/>
<GradientStop Color="#EEE" Offset="0.1"/>
<GradientStop Color="#EEE" Offset="0.9"/>
<GradientStop Color="#FFF" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<SolidColorBrush x:Key="DisabledForegroundBrush" Color="#888" />
<SolidColorBrush x:Key="DisabledBackgroundBrush" Color="#EEE" />
<SolidColorBrush x:Key="WindowBackgroundBrush" Color="#FFF" />
<SolidColorBrush x:Key="SelectedBackgroundBrush" Color="#DDD" />
<!-- Border Brushes -->
<LinearGradientBrush x:Key="NormalBorderBrush" StartPoint="0,0" EndPoint="0,1">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#CCC" Offset="0.0"/>
<GradientStop Color="#444" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<LinearGradientBrush x:Key="HorizontalNormalBorderBrush" StartPoint="0,0" EndPoint="1,0">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#CCC" Offset="0.0"/>
<GradientStop Color="#444" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<LinearGradientBrush x:Key="DefaultedBorderBrush" StartPoint="0,0" EndPoint="0,1">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#777" Offset="0.0"/>
<GradientStop Color="#000" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<LinearGradientBrush x:Key="PressedBorderBrush" StartPoint="0,0" EndPoint="0,1">
<GradientBrush.GradientStops>
<GradientStopCollection>
<GradientStop Color="#444" Offset="0.0"/>
<GradientStop Color="#888" Offset="1.0"/>
</GradientStopCollection>
</GradientBrush.GradientStops>
</LinearGradientBrush>
<SolidColorBrush x:Key="DisabledBorderBrush" Color="#AAA" />
<SolidColorBrush x:Key="SolidBorderBrush" Color="#888" />
<SolidColorBrush x:Key="LightBorderBrush" Color="#AAA" />
<!-- Miscellaneous Brushes -->
<SolidColorBrush x:Key="GlyphBrush" Color="#444" />
<SolidColorBrush x:Key="LightColorBrush" Color="#DDD" />
<ControlTemplate x:Key="ComboBoxToggleButton" TargetType="ToggleButton">
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition />
<ColumnDefinition Width="20" />
</Grid.ColumnDefinitions>
<Border
x:Name="Border"
Grid.ColumnSpan="2"
CornerRadius="2"
Background="{StaticResource NormalBrush}"
BorderBrush="{StaticResource NormalBorderBrush}"
BorderThickness="1" />
<Border
Grid.Column="0"
CornerRadius="2,0,0,2"
Margin="1"
Background="{StaticResource WindowBackgroundBrush}"
BorderBrush="{StaticResource NormalBorderBrush}"
BorderThickness="0,0,1,0" />
<Path
x:Name="Arrow"
Grid.Column="1"
Fill="{StaticResource GlyphBrush}"
HorizontalAlignment="Center"
VerticalAlignment="Center"
Data="M 0 0 L 4 4 L 8 0 Z"/>
</Grid>
<ControlTemplate.Triggers>
<!--<Trigger Property="ToggleButton.IsMouseOver" Value="true">
<Setter TargetName="Border" Property="Background" Value="{StaticResource DarkBrush}" />
</Trigger>-->
<Trigger Property="ToggleButton.IsChecked" Value="true">
<Setter TargetName="Border" Property="Background" Value="{StaticResource PressedBrush}" />
</Trigger>
<Trigger Property="IsEnabled" Value="False">
<Setter TargetName="Border" Property="Background" Value="{StaticResource DisabledBackgroundBrush}" />
<Setter TargetName="Border" Property="BorderBrush" Value="{StaticResource DisabledBorderBrush}" />
<Setter Property="Foreground" Value="{StaticResource DisabledForegroundBrush}"/>
<Setter TargetName="Arrow" Property="Fill" Value="{StaticResource DisabledForegroundBrush}" />
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
<ControlTemplate x:Key="ComboBoxTextBox" TargetType="TextBox">
<Border x:Name="PART_ContentHost" Focusable="False" Background="{TemplateBinding Background}" />
</ControlTemplate>
<Style x:Key="{x:Type ComboBox}" TargetType="ComboBox">
<Setter Property="SnapsToDevicePixels" Value="true"/>
<Setter Property="OverridesDefaultStyle" Value="true"/>
<Setter Property="ScrollViewer.HorizontalScrollBarVisibility" Value="Auto"/>
<Setter Property="ScrollViewer.VerticalScrollBarVisibility" Value="Auto"/>
<Setter Property="ScrollViewer.CanContentScroll" Value="true"/>
<Setter Property="MinWidth" Value="120"/>
<Setter Property="MinHeight" Value="20"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="ComboBox">
<Grid>
<ToggleButton
Name="ToggleButton"
Template="{StaticResource ComboBoxToggleButton}"
Grid.Column="2"
Focusable="false"
IsChecked="{Binding Path=IsDropDownOpen,Mode=TwoWay,RelativeSource={RelativeSource TemplatedParent}}"
ClickMode="Press">
</ToggleButton>
<ContentPresenter
Name="ContentSite"
IsHitTestVisible="False"
Content="{TemplateBinding SelectionBoxItem}"
ContentTemplate="{TemplateBinding SelectionBoxItemTemplate}"
ContentTemplateSelector="{TemplateBinding ItemTemplateSelector}"
Margin="3,3,23,3"
VerticalAlignment="Center"
HorizontalAlignment="Left" />
<TextBox x:Name="PART_EditableTextBox"
Style="{x:Null}"
Template="{StaticResource ComboBoxTextBox}"
HorizontalAlignment="Left"
VerticalAlignment="Center"
Margin="3,3,23,3"
Focusable="True"
Background="Transparent"
Visibility="Hidden"
IsReadOnly="{TemplateBinding IsReadOnly}"/>
<Popup
Name="Popup"
Placement="Bottom"
IsOpen="{TemplateBinding IsDropDownOpen}"
AllowsTransparency="True"
Focusable="False"
PopupAnimation="Slide">
<Grid
Name="DropDown"
SnapsToDevicePixels="True"
MinWidth="{TemplateBinding ActualWidth}"
MaxHeight="{TemplateBinding MaxDropDownHeight}">
<Border
x:Name="DropDownBorder"
Background="{StaticResource WindowBackgroundBrush}"
BorderThickness="1"
BorderBrush="{StaticResource SolidBorderBrush}"/>
<ScrollViewer Margin="4,6,4,6" SnapsToDevicePixels="True">
<StackPanel IsItemsHost="True" KeyboardNavigation.DirectionalNavigation="Contained" />
</ScrollViewer>
</Grid>
</Popup>
</Grid>
<ControlTemplate.Triggers>
<Trigger Property="HasItems" Value="false">
<Setter TargetName="DropDownBorder" Property="MinHeight" Value="95"/>
</Trigger>
<Trigger Property="IsEnabled" Value="false">
<Setter Property="Foreground" Value="{StaticResource DisabledForegroundBrush}"/>
</Trigger>
<Trigger Property="IsGrouping" Value="true">
<Setter Property="ScrollViewer.CanContentScroll" Value="false"/>
</Trigger>
<Trigger SourceName="Popup" Property="Popup.AllowsTransparency" Value="true">
<Setter TargetName="DropDownBorder" Property="CornerRadius" Value="4"/>
<Setter TargetName="DropDownBorder" Property="Margin" Value="0,2,0,0"/>
</Trigger>
<Trigger Property="IsEditable"
Value="true">
<Setter Property="IsTabStop" Value="false"/>
<Setter TargetName="PART_EditableTextBox" Property="Visibility" Value="Visible"/>
<Setter TargetName="ContentSite" Property="Visibility" Value="Hidden"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
<Style.Triggers>
</Style.Triggers>
</Style>
</Window.Resources>