Connecticut requires you to have earned at least 40 times the WBA. The minimum WBA is $15, so the minimum amount you must earn in the entire base period is $600. The WBA is computed by multiplying the HWQ by 1/26.
Therefore, you must have worked during at least one quarter of the base period in order to qualify for unemployment insurance in Connecticut.
Connecticut offers both an extended base period and an alternate base period. The alternate base period uses the last four completed calendar quarters of the base period. The extended base period uses the last four completed calendar quarters of the base period before you were injured/disabled/sick.
In Connecticut an employer or employing unit is covered under unemployment insurance if it paid at least $1,500 in wages during any calendar quarter in the current or previous calendar year. Further, an employer/employing unit is also covered under unemployment insurance if it paid wages to at least one employee and employed said worker at least one day per week during the 20 weeks of the current or previous calendar year.