On May 31, 2012, the state of Connecticut became one of the several US states On May 31, 2012, the state of Connecticut became one of the several US states that have approved the use of medical marijuana. Governor Dannel P. Malloy signed the bill into law after the House and Senate showed majority support for it. If you are a resident of Connecticut and at least 18 years old, you may apply to be part of the medical marijuana program in the state. However, if you are a prison inmate or ...