While notice to quit in response to a tenant's complaint about a handyman's possible unlawful entry of a unit might be given in retaliation for that report to the landlord, that does not make it a retaliatory eviction as contemplated by law as a defense to the termination of tenancy. I do not see a provision of CGA Sec. 47a-20 that would apply to the facts you describe.
In terms of any theft that occurs from the tenant's premises subsequent to the landlord's being informed of the issue, whether by the tenant or previously by others raising substantially similar allegations, the tenant should be able to pursue a negligence action against the landlord for retaining an employee who the landlord understands to be improperly entering tenants' units and stealing from them.

