Since you say the tenant only gave you 3 days notice, does this mean they notified you on Nov. 27 and moved out by Dec. 1? Based on the statute Jet posted, it looks like you would then have them on the hook for 27 days of rent in December, unless you re-rented the unit before then. I base this on the portion of the law that says notice is not void if the terminating day does not correspond with the end of a rental period. Again, here's the statute regarding withholding security deposit:
554.612 Response to notice of damages.
If a landlord claims damages to a rental unit and gives notice of damages as required, the tenant upon receipt of the list of damages shall respond by ordinary mail to the address provided by the landlord as required by section 3 within 7 days, indicating in detail his agreement or disagreement to the damage charges listed. For the purposes of this section the date of mailing shall be considered the date of the tenant's response.
554.613 Action for damages; retention of security deposit; waiver.
(1) Within 45 days after termination of the occupancy and not thereafter the landlord may commence an action in a court of competent jurisdiction for a money judgment for damages which he has claimed or in lieu thereof return the balance of the security deposit held by him to the tenant or any amount mutually agreed upon in writing by the parties. A landlord shall not be entitled to retain any portion of a security deposit for damages claimed unless he has first obtained a money judgment for the disputed amount or filed with the court satisfactory proof of an inability to obtain service on the tenant or unless:
(a) The tenant has failed to provide a forwarding address as required by section 11.
(b) The tenant has failed to respond to the notice of damages as required by section 12.
(c) The parties have agreed in writing to the disposition of the balance of the deposit claimed by the landlord.
(d) The amount claimed is entirely based upon accrued and unpaid rent equal to the actual rent for any full rental period or portion thereof during which the tenant has had actual or constructive possession of the premises.
(2) This section does not prejudice a landlord's right to retain any security deposit funds as satisfaction or partial satisfaction of a money judgment obtained pursuant to summary proceedings filed pursuant to chapter 57 of Act No. 236 of the Public Acts of 1961, as amended, being sections 600.5701 to 600.5759 of the Compiled Laws of 1948 or other proceedings at law. Failure of the landlord to comply fully with this section constitutes waiver of all claimed damages and makes him liable to the tenant for double the amount of the security deposit retained.
So, based on this, you can withhold the deposit for rent. For damages you need to send the tenant a statement of damages, and they have a chance to say they didn't do it. If they say they didn't do it, you need a money judgment. Act quickly after the 27th, it looks like you only have 45 days to file the action and must give the tenant 7 days to respond.