I'm unsure from your post if the lease expired or not. If it has expired, you must evict them as holdover tenants. You won't get back rent awarded, since they paid the rent. (You just haven't cashed the check.)
If the lease is still going, you have to bribe the tenants to leave.
You can contact the local tenant/landlord association for help finding the proper forms to evict tenants. You may also be able to buy an eviction kit for CT -- forms & instructions. Then begin the eviction. Here are the CT landlord tenant laws:
http://www.cslnet.ctstateu.edu/statutes/title47a/httoc.htm
=============================
Sec. 47a-3d. (Formerly Sec. 47-22). Holding over not evidence of new lease.
Holding over by any lessee, after the expiration of the term of his lease, shall not be evidence of any agreement for a further lease. Parol leases of lands or tenements reserving a monthly rent and in which the time of their termination is not agreed upon shall be construed to be leases for one month only.
Sec. 47a-23. (Formerly Sec. 52-532). Notice to quit possession or occupancy of premises.
Form. Delivery. Federal termination notice. (a) When the owner or lessor, or his legal representative, or his attorney-at-law, or in-fact, desires to obtain possession or occupancy of any land or building, any apartment in any building, any dwelling unit, any trailer, or any land upon which a trailer is used or stands, and (1) when a rental agreement or lease of such property, whether in writing or by parol, terminates for any of the following reasons: (A) By lapse of time; (B) by reason of any expressed stipulation therein; (C) violation of the rental agreement or lease or of any rules or regulations adopted in accordance with section 47a-9 or 21-70; ... or (4) when an action of summary process or other action to dispossess a tenant is authorized under subsection (b) of section 47a-23c for any of the following reasons: (A) ... (C) bona fide intention by the landlord to use such dwelling unit as his principal residence; by the landlord to use such dwelling unit as his principal residence; or ... such owner or lessor, or his legal representative, or his attorney-at-law, or in-fact, shall give notice to each lessee or occupant to quit possession or occupancy of such land, building, apartment or dwelling unit, at least five days before the termination of the rental agreement or lease, if any, or before the time specified in the notice for the lessee or occupant to quit possession or occupancy.
(b) The notice shall be in writing substantially in the following form: "I (or we) hereby give you notice that you are to quit possession or occupancy of the (land, building, apartment or dwelling unit, or of any trailer or any land upon which a trailer is used or stands, as the case may be), now occupied by you at (here insert the address, including apartment number or other designation, as applicable), on or before the (here insert the date) for the following reason (here insert the reason or reasons for the notice to quit possession or occupancy using the statutory language or words of similar import, also the date and place of signing notice). A.B.".
------------------
This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.
