According to a number of resources, including the link below, the State of Massachusetts has two national flags but no state flag.
I also have the following letter:
Commonwealth of Massachusetts
Cambridge, May 11, 1865
Lient. Geo. W. Taylor
Comd'g 4th Mafs Battery
Your communication dated April 19th addressed to the Adjutant General in reference to State Guidon has been referred to me; and I would respectfully inform you in answer to the same, that the State Guidon is not in the Department and I have no knowledge of ever receiving it; we have two National Guidons returned by your Battery.
I have the honor etc
Chf. Clk. Dpt.