Are there any other ways to detect collision between two objects besides the bounding rectangle method and downloading another class to put into Android?
Android does not limit your options when it comes to collision detection.
Here is a nice article about SAT collision detection: http://www.codeproject.com/Articles/15573/D-Polygon-Collision-Detection
That implementation also has the nice feature of being tunneling free. That is, if two object with very high speed intersect each others paths in such a way that they will overlap in the current frame, it will still detect it as an collision.
I think you need to rephrase your question. Are you going to do 3d collision detection, is the performance important, are there any special properties of your polygons (eg, maybe they are concave instead of convex?)
What is it that you want to do with collision detection?
Refer the below site for some guidance:
It explains bounding shapes that will be used to check for collision. In the case of our robot, we will be using four bounding rectangles. I will suggest to give more specific requirement so that I can update my answer more helpfully.