Did US tank crews in WWII get issued Tommy Guns like in the movies?

Yes, up to a certain point. The M3 medium tank had provisions for two .45 caliber Thompson submachine guns. One was mounted underneath the bow machine guns to the left of the radio operator’s seat, and the second was mounted in the right rear of the fighting compartment. These could be fired from the pistol ports or through the hull side doors (later welded shut, and then eliminated altogether), or used outside the tank. 1,200 rounds of .45 caliber ammunition were carried. Two M2 tripods were carried on the outside of the tank, so the bow machine guns could be dismounted. The M3 and M5 light tanks had provisions for a single Thompson submachine gun, first carried in the right rear of the fighting compartment. When the redesigned M5A1 light tank received a new turret, the submachine gun was carried atop the radio which was mounted in the rear. 420-540 rounds of .45 caliber ammuntion were carried, depending upon the turret configuration. The 50-round drum magazines used in earlier vehicles were replaced by 30-round stick magazines. The M4 medium tank initially carried one Thompson submachine gun, stored atop the radio in the rear of the turret, with 600 rounds of ammunition. Two tripods, one for the .50 caliber antiaircraft machine gun and one for the .30 caliber bow or coaxial machine gun were also carried.

The M3 submachine gun (“Grease Gun”) nominally replaced the M1928A1, M1, and M1A1 Thompson as the U.S. Army’s submachine gun of choice in December 1942, but it took until late 1944 to almost fully supplant the latter in service. The “next generation” M4 Sherman (47-degree front hull, and “wet” ammunition stowage where applicable) introduced in early 1944 had provisions for five M3 submachine guns, one for each crew member. 900 rounds of .45 caliber ammunition were carried in 30-round magazines (and unlike earlier vehicles like the M3 medium, which had ammunition scattered in locations throughout the vehicle) evenly divided and placed into five individual carrying bags, two in the turret and three in a storage box in the hull. Units such as the 6th Armored Division, equipped with earlier variants of the M4 while waiting in England before D-Day, fabricated racks for M3 submachine guns in their vehicles.

U.S. tank crew members were otherwise unarmed, but even though all crew members now were at least assigned individual weapons, it still became an issue locating them when having to abandon the tank quickly; observers stressed that all crew members should have pistols in shoulder holsters on their person at all times.

(8) Personal equipment: In tank casualties of this unit and from information gathered from other units, each tank has burned when hit and does not permit personnel to evacuate any equipment other than that carried on the person. Therefore, it would be a great saving to the Government and afford future protection to the personnel, for the individual arm of each tank crew member to be the automatic pistol with shoulder holster, in lieu of the Thompson Sub-Machine gun M-3 [sic] as now authorized. It is highly desirable, however, that one (1) sub-machine gun M-3 be an intregate [sic] part of the equipment of the tank.

Sources:

Hogg, Ian V. The American Arsenal: The World War II Official Standard Ordnance Catalogue. Barnsley: Frontline Books, 2014.

United States. United States Army. War Department Technical Manual 9-726 Light Tank M3. Washington, D.C.: United States Government Printing Office, 1942.

United States. United States Army. War Department Technical Manual 9-750 Medium Tanks M3, M3A1, and M3A2. Washington, D.C.: United States Government Printing Office, 1942.

United States. United States Army. War Department Technical Manual 9-754 Medium Tank M4A4. Washington, D.C.: United States Government Printing Office, 1943.

United States. United States Army. War Department Technical Manual 9-759 Medium Tank M4A3 (September 1944). Washington, D.C.: United States Government Printing Office, 1944.

United States. United States Army. After Action Report - August 1944. By Ralph Talbot III, Lt. Col., 702nd Tank Bn., Commanding. N.p.: 1944.

Zaloga, Steven J. US Army Tank Crewman 1941–45: European Theater of Operations (ETO) 1944–45. Oxford: Osprey Publishing, 2004.

Bearing in mind that tanks tend to be cramped places, the issue weapons would have been as small as possible. There are stowage points built into the tank to hold the weapon and ammunition, specifically designed for the type of weapon.

Initially, US crews were equipped with the M1928 Thompson SMG, but it is large and expensive to make. It was replaced on issue by the M3 “Grease Gun” to tank crews, this cheaper weapon saw service in some US tanks through the end of the century. Depending on when the tank was manufactured, it came with racks for the one type of weapon or the other. You cannot easily put an M1 carbine and magazine into an M1928 rack. It probably can be done with effort, but it isn’t issue.

That said, us tankers will gleefully appropriate anything not glued down, and we’re very resourceful. (Remember, STEAL is merely an acronym for “Supplies Taken in Excess of Authorized Listings”), and it would not be massively hard for a crew, if they wanted to, to acquire a carbine for whatever reason, probably relating to picket duties and the like. Normally we just view the small arms as something to keep the other guy’s head down while we run away and get another tank. The SMGs are fine for this, obviously an opinion shared by the procurement and design folks at Ordnance.

Of course, every crewman was also issued a sidearm, worn in the traditional “tanker holster” on the chest. (It is less likely to get in the way of hatches and the like. Also still used today)