It may be as bad or worse in Connecticut right now.
In CT, you cannot buy ammunition without a state-issued firearms ID card. I'm sure each card probably has a unique barcode imprinted on it, as a driver's license has (I don't have one).
So... I'm guessing that when you do buy ammo in CT, you're going to have to present the ID card along with your purchase (cash, or otherwise).
I'm not sure if the card gets scanned or recorded with the purchase, but I'm thinking it probably does. Again, I don't have one so I've never observed the process in the gun shop.
So... Connecticut is probably tracking individual ammo purchases. Card, cash, or whatever...
(I welcome correction)