I need to develop an application using Google Maps
in Android to locate my current location and need to find nearest location.
(For example: Nearby police station from my current location.)
It should accept my current location and output should display nearest place.
Can anyone help me to give some suggestion,links,tutorial to do that?
First go through this tutorial for getting familiar with Android Google Maps and this for API 2.
To retrive the current location of device see this answer or this another answer and for API 2
Then you can get places near by your location using Google Place API and for use of Place Api see this blog.
After getting Placemarks of near by location use this blog with source code to show markers on map with balloon overlay with API 2.
You also have great sample to draw route between two points on map look here in these links Link1 and Link2 and this Great Answer.
After following these steps you will be easily able to do your application. The only condition is, you will have to read it and understand it, because like magic its not going to be complete in a click.