In NY, you can vote in any jurisdiction in which you have a residence, but you have to choose which one. This has become contentious recently as largely Republican upstate towns have been trying to disenfranchise largely Democratic vacationers.
CT has a more lenient statute — you can vote in town elections in any and all towns in which you own property as long as you are a US Citizen. Nonresident property owners often vote down school and town budgets.