Is your Polygon a Graphic or a Feature? Both can be selected, but you will need to know what you are trying to select.
Here's one example of selecting Features from a FeatureLayer by performing a spatial query - selecting all features within a certain buffer distance of a point - Edit features—ArcGIS Runtime SDK for Android | ArcGIS for Developers .
If you are working with Graphics, there is no equivalent method that will query and select graphics in a GraphicsOverlay. However, you can use the Graphic.setSelected method to select an individual Graphic. You can get a reference the Graphic that a user tapped on as shown in this sample - Identify Graphics Hittest—ArcGIS Runtime SDK for Android | ArcGIS for Developers - so you could just add the call to setSelected to that sample code to see how it works.
Hope this helps,