What weapons are police departments allowed?

Are there any statute limits to what weapons municipal police departments are allowed to possess? Afaik, they all are allowed to stock automatic firearms for special use, and I’ve heard of the police using armored vehicles as battering rams, but what else? I would presume that heavy military ordinance would be used so rarely that if it came to that the state National Guard would be called in. But would a S.W.A.T. team for a big city like New York or Los Angeles have for example hand grenades? Grenade launchers? Shoulder-launched rockets? Mortars? Howitzers? Automatic cannon? How far up the armament scale do police usually go? Are there any federal laws that police can’t have ground-attack aircraft, heavy artillery or main battle tanks?

The Philadelphia police department famously dropped a bomb on a row house back in 1985, but that was a one-time thing.

I would imagine it depends on the local laws, but apparently there is a Federal program to donate surplus military weaponry to local law enforcement departments, including grenade launchers. They use them for tear gas, though.

Police used to only keep very limited weaponry. During the North Hollywood Shootout in 1997, police found themselves outgunned and had to raid local gun shops for weapons and ammunition just to stop two bank robbers. After that, a lot of police departments did a bit of a re-think, and stocked up on some heavier military style weaponry just in case anything like that ever happened in their jurisdiction.

I would think that budgets limit their choice of equipment more than any laws would. Keeping a main battle tank on standby is expensive. There have been a couple of cases of guys stealing tanks and going on a rampage, though, so having something in your arsenal that can take out a tank isn’t necessarily as far fetched as you might initially think.

By the way, the wikipedia page for SWAT does list the weapons and vehicles that they are likely to use. They have a picture of an armored vehicle that they can use for combat and rescue.

Well, I believe there is a Federal prohibiting them from possessing nuclear weapons.

Not that any local police department is likely to be able to afford one. In fact, budget is probably the largest restriction on what weapons police departments can have. Especially given that they should be able to get heavier weapons from the nearest National Guard Armory if they are ever needed.