What do I need in order to buy ammo in NY?

Money.

If you're trying to buy ammo that can be used in a handgun, they might want to see a pistol license, but you can usually talk your way out of that by explaining it's for a carbine.

Okay, sounds good.  In CT they want a god damn pistol permit or ammo license or some shit, so I just wanted to be sure.  Thank you for the info.

Some sporting goods stores ask for pistol permit if buying handgun ammo, if they ask it's for a rifle.

In CT, non residents can obtain the Ammunition Certificate (see this link for application) which will allow them to buy ammunition and ammunition magazines in that state. Note that in CT its only a requirement to show one of the relevant permits/certificates when purchasing ammo. There is no prohibition on being given or gifted ammo as long as no money or monetary service is exchanged

I've crossed the border to purchase ammo in NY without issue. Like others have said if they ask if its for a handgun, tell them no. One counter drone tried to quiz me on buying 9mm and I told him it was for a Marlin Camp Carbine.

You can quote me on this:  "Fuck Connecticut and their ammunition Laws" in fact fuck them all together.
Under un-SAFE we were supposed to be subjected to a "back ground check" prior to purchasing ammunition in NY, buy as usual (and to our advantage) the legislature screwed the pooch thinking they'd piggy-back on the NICS system, but that blew up in their faces....maybe just as well, because if the Fudds had to submit before they could by a flat of Trap loads they'd whine even more while blaming it on the back rifle owners.