At the state level you should not have to pay income tax to both states for the same dollar of income. One issue is will your employer in Connecticut withhold New York State income tax, but that only impacts where the funds will flow when you file your state tax returns.
In general when a person lives in one state and works in the other, unless the states have an agreement, both will try and claim the income but give a credit for the amount you pay to the other state. So just figure you will end up paying money to the state that wants more in taxes.
Most people don't consider the state tax impact when determining the split between Roth and pre-tax retirement contributions. This is because the federal tax rate is almost always higher than the state tax rate.
In a related note:
Because you graduated in May and you make $77,000, you might not be eligible for the Retirement Savings Contributions Credit (Saver’s Credit)
Who's eligible for the credit?
You're eligible for the credit if you're:
- Age 18 or older,
- Not claimed as a dependent on another person’s return, and
- Not a student.
You were a student if during any part of 5 calendar months of the tax
year you:
- Were enrolled as a full-time student at a school, or
- Took a full-time, on-farm training course given by a school or a state, county, or local government agency.
A school includes technical, trade, and mechanical schools. It does
not include on-the-job training courses, correspondence schools, or
schools offering courses only through the Internet.
There are also income limits.
But check the forms. If you do qualify for the credit, it might make sense to increase your contributions.