After successfully qualifying NEET PG, you can either register for all india counselling (for 15% AIR) or state counselling (85% state quota), or chose both.

Domicile candidates of a particular state are eligible for virtually all the seats available in their category. This includes government as well as management seats in government and private colleges.

Non domicile candidates (like you) can surely apply to another state for MDS counselling (Maharashtra in your case) but you will only be eligible for the management seats in private colleges.