Obviously, the landlord can try to evict you, as you are realizing even without proof. You can fight the eviction by responding that you are not smoking and not violating the terms of the rental agreement. The burden of proof is on the landlord to prove that you violated the terms of the lease by a preponderance of the evidence. However, it will definitely be a "he said/he said" situation. As a former judge who presided over evictions, I highly recommend that you get an attorney. There are plenty of excellent attorneys here on Avvo. Use the Find a Lawyer option to find a good attorney to fight this.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice.
You can dispute your Landlord's allegations by filing an answer to the eviction lawsuit. It is his burden to prove that you have violated the terms of your lease and that such violation permits him to obtain a judgment for possession of the leased premises. If you are not under a lease (or it has expired or is expiring), there may not be much you can do to prevent him from forcing you to move, but you still can dispute the allegations that you've smoked in your rental unit and demand that no charges be assessed against your security deposit for smoke related damages.
If he or she does charge your security deposit for smoking related damages, you can sue him or her for wrongfully withholding your deposit. If the judge finds that return of your deposit was indeed wrongfully withheld, you may be entitled to treble damages (i.e., 3 times the amount wrongfully withheld).
Proof is required for the landlord to prevail, but he or she only needs to "tip the scales" -- showing that it is more likely than not that you smoked in the unit. The letter you mention could help you "tip the scales" in your favor, as well as, perhaps, testimony from guests you've had over, that have known you for a while, that could testify under oath that you do not smoke and that while they were at your house, they noticed smoke coming into your apartment from other units.
Best of luck.
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If your landlord files a forcible detainer (eviction) action, be sure to attend the return date, file an answer, and request a hearing. If you want a jury trial, you need to as for one when you file your answer and pay a jury fee. At the hearing the judge (or the jury if you asked for one) would decide if the landlord has grounds to evict you.