I dont know about assault rifles but Hamilton Rod & Gun in Sturbridge, MA has a shooting range that is either 200 or 300 meters long, distance is going by what was said to me. I have been there a couple of times, its a big range, not your typical shooting range in MA. Judging by the distance of the range, they allow high-powered rifles. I belong there and its a great club. Bring a conversion table for meters to yards.
New Bedford police have a range that is in Dartmouth which has a civilian side where you can shoot rifles. When I was there for my academy shooting I saw a couple of freaks come out of the civilian side with rifles. Not sure how you go about joining....maybe call them
It would really help if you stated where in the State you were looking to shoot?
I do NOT know of any gun clubs in the SE part of the state that put any restrictions on what kind of rifle you can use (IF they have a high power rifle range)!
Braintree R&P has a 50/100yd Rifle range (NO pistols allowed on this range) as well as 6 other ranges (including two state-of-the-art indoor ranges, jacketed pistol ammo allowed, no CF rifles indoors). They hold CMP shoots each month (except for Winter) where you are REQUIRED to use a military assault rifle (M1, AR15, etc.). Lots of LEOs belong there. Safety rules are VERY strict and they have the best indoor range in the state. www.brp.org I've been a member for 6+ years and highly recommend this place. If you want any further info, just ask.
Ames R&P (in North Easton) has a 50/100 yd and a 200/300 yd range. They also run monthly CMP shoots with M1s and AR15s. Club is "OK" but BOD keeps changing the rules on what you can/can't do on a regular basis and without any input from members. I've been a member here for 4-5 years and each year I contemplate dropping out rather than renewing. http://www.amesriflepistolclub.net/
Auburn rod and gun club, Singeltary rod and gun club in Sutton, 8 point rod and gun club in Sterling, all require membership. If you are a full-time PO you can shoot at either with no problem, but don't get crazy with the rapid firing or you will get the boot.
Marlboro Fish & Game must allow rifles because when my dad was sighting in the M-4 in his cruiser, he sighted it in at the Marlboro Fish & Game. I dont know if they allow fully automatic rifles. I know that Nimrod League of Holden on the Princeton/Holden line shuts down its grounds once in a while to let the Princeton police shoot up there. I dont know if the POs that shoot up there shoot their rifles and I am not sure if the club allows fully auto rifle either.
Numbers and addresses to clubs suggested:
Hamilton Rod & Gun - 508-347-3389
24 Hamilton Road
Sturbridge, MA 01566-2954
Marlboro Fish & Game - 508-485-9739
1 Muddy Lane
Marlborough, MA 01752
Nimrod League of Holden - 978-464-2622
168 Coal Kiln Road
Princeton, MA 01541