Is marijuana legal in Connecticut? Yes, the state of Connecticut is one of the two dozen US states that have legalized marijuana for use in various medical treatments. The law was signed into law on May 31, 2012, after receiving majority support in the House and the Senate.Who can use, possess, grow, etc. legal marijuana in Connecticut? People suffering from certain medical conditions can apply to be a part of Connecticut's medical marijuana program. Those that want to work as caregivers ...