You will need to file a New York resident tax return and a Connecticut non-resident return.  Complete your Connecticut nonresident return first.  In New York, your resident state, you will be taxed on all income you received while a resident of New York (including your CT earnings) however you will get a credit for taxes paid to Connecticut.  This credit will be calculated on  Form IT-112-R New York State Resident Credit.

I work in CT.  Live in the Bronx, NY area.   I had CT State and City taxes deducted from paycheck and NYC taxes taken out.  NO NY State taxes??

Should I set a side $50.00 a week for State taxes to be on the safe side when I file my 2022 tax return??

Thank you

Have a nice day

NY will give you a credit for most of what you pay CT. But since NY has a slightly higher rate,  there should be little tax due at tax filing time.  You  can  do a rough estimate based on these tables:

https://www.forbes.com/advisor/income-tax-calculator/new-york/#:~:text=The%20state%20income%20tax%20....

https://www.incometaxpro.net/tax-rates/connecticut.htm

There is no underpayment penalty if you owe less than $300.