If you live in Maine, you do not need to file a MA tax return for your retirement income - it doesn't make any difference where the checks are coming from or from where you earned the retirement.
Effective for retirement income received after December 31, 1995, federal law prohibits any state from taxing certain retirement income (mainly pension income) unless you are resident of, or domiciled in, that state. For example, if you receive a pension from your former California employer and you now reside in New Mexico, California may not tax your retirement income - but New Mexico can. Because you are now a New Mexico resident, your retirement income is taxable in New Mexico.