How old do you have to be to be a bartender in Connecticut?

you can legally bar tend in Connecticut at 18

HOWEVER... the majority of bars would likely think twice about hiring someone as a bar tender that can't legally taste what they are mixing. Many major national chains also have general policies of 21+ so they don't have to worry about liability or differences between states.

you generally won't be hired as a bar tender anyway... you would almost certainly get hired as a server or bar back, and after a period of time learning the ropes they would start giving you more and more responsibility.