When you edit the control template of the RadDropDownButton you will see the control ButtonChrome. This control holds all visual states for the RadDropDownButton control. Please find the following attached files:
In the raddropdownbutton-style.zip file you will find a custom style for RadDropDownButton control.
In the blend.png file you will find which brushes have to be changed for the checked state.
If you have further questions please do not hesitate to ask us.
I hope this will help you.
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