On quick google I'm seeing a requirement to have worked Five quarters, but I would double check the elgibility requirements online - ctpaidleave.org

"Answer: An employee becomes eligible for Paid Leave benefits if they have earned wages of at least $2,325 in the highest-earning quarter of the first four of the five most recently completed quarters (the "base period”) and they are currently employed with a covered Connecticut employer. Those not employed, but had been employed by a covered Connecticut employer within the last 12 weeks, or those in Connecticut who are self-employed/sole proprietor and has enrolled in the program. "