Is Social Security the only income for the year you had? If so, you would not have a filing requirement.
The amount of time you lived in CT doesn't affect your filing requirement. The number of days determines your residence status.
Per Connecticut: If you changed your legal residence to another state but continued to maintain a permanent place of abode in Connecticut for the entire year and spent more than 183 days in Connecticut in the aggregate during the taxable year, you will be considered to be a resident for that year.
This link will give you additional information on your filing requirement:
Connecticut Part-Year Resident