how to change the color of a particular area on Google map api v2 in android

I am working on an Android app that makes use of the Google Maps API v2 and would like to mark a specific area on the map with a certain color on a click event. For example, when I click on India, the area covering the country should be colored green.

I'm already using GroundOverlay, but it requires an image to display something on the map, resulting in the colored area not being a good match. Since both the map and the image have their own shape, this does not cover the exact area.

Can anyone please tell me how to color an Android Google Maps API v2 map more accurately?