Here is the statute. He can't enter your apartment when you're not there if you don't want him to. Unfortunately, this is an old statute, and hard to follow:
Sec. 47a-43. (Formerly Sec. 52-462). Complaint and procedure: Forcible entry and detainer; entry and detainer. (a) When any person (1) makes forcible entry into any land, tenement or dwelling unit and with a strong hand detains the same, or (2) having made a peaceable entry, without the consent of the actual possessor, holds and detains the same with force and strong hand, or (3) enters into any land, tenement or dwelling unit and causes damage to the premises or damage to or removal of or detention of the personal property of the possessor, or (4) when the party put out of possession would be required to cause damage to the premises or commit a breach of the peace in order to regain possession, the party thus ejected, held out of possession, or suffering damage may exhibit his complaint to any judge of the Superior Court.
(b) Such judge shall forthwith issue a summons to the party complained of, directed to some proper officer, to notify him to appear at a specified time and place, within eight days from the exhibition of such complaint, in the superior court for the judicial district wherein the injury complained of was done, to answer to the matters contained in the complaint.
(c) Such summons shall be served upon the party complained of six days inclusive before the day appointed for trial.
(d) If, after service of such summons, the party complained of does not appear and defend, the judge shall proceed in the same manner as if he were present.
In addition, here's what it says in more "layperson" language in that website I sent to you, above:
I was hunging hard for the statute, because I didn't want to give you ONLY the lay version:
Can my landlord enter my apartment without my consent?
No. Your landlord can never enter your apartment without your permission unless
- there is an genuine emergency (for example, water is leaking into the apartment below yours). During an emergency, the landlord can enter at any time
- the landlord has a court order giving him/her permission to enter.
- you have abandoned the apartment and moved out
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The landlord cannot under any circumstances enter your apartment to harass or bother you. If s/he does, you should call the police and file a complaint.
The law expects you to give consent for the landlord to enter if the landlord's request is reasonable. For a request to be reasonable, the landlord must:
- Give you reasonable advance notice, either orally or in writing,
- Ask for entry only at a reasonable time, and
- Ask for entry only for one or more of the following reasons
- o To make necessary or agreed-upon repairs
- o To inspect the premises
- o To show the apartment to buyers of the building, workers or contractors, or prospective tenants.
If you unreasonably refuse to let the landlord enter, the landlord is not allowed to enter anyway. The landlord must go to court and get a court order allowing him/her to enter.
Reference Source: http://www.jud.ct.gov/faq/landlord.html
May I be of further help?