Do you need a test to verify that the part has been coated vs. non-coated, or a test to verify the coating on the part is manganese phosphate as opposed to some other coating (such as zinc phosphate)?
If it is the first case, then the visual process or the chemical process CoryPad mentioned will work.
The second case is a bit more complex. While I am sure there are spot tests for manganese phosphate, I am not aware of any specific ones.
If I were given the problem, I'd control the process and verify coating immediately after it was applied. It the part comes out of a manganese phosphating bath, and is covered with an acceptable coating, you can be pretty sure is has a manganese phosphate coating on it.
rp