I know that I have to file state returns for both. My question is CT took out $1,950 in state taxes, and MA only took out $193. Do I have to pay Ma income tax even if I worked in CT for the full year? Thank you for any help you can give me on this.

You will have to pay CT tax in full.

MA should give you a credit for the CT taxes paid, which is probably why the withhholding was so small.