Live in CT, work in NY

Hello,

 

Ive read through numerous other postings here regarding living in CT and working in NY, but I am still a bit unclear based on my situation. I currently live in CT, and work in the state of NY (not NYC). On my paychecks, taxes are withheld for both CT (a smaller amount) and NY. Does this seem right? I thought I would be paying NY income tax, and filing for a resident return there and using that as credit toward by owed CT income tax? Just a bit confused now why I am paying tax in both currently. Any knowledge is hugely appreciated!