A lease not renewing is NOT AN EVICTION. That's really key when you read NH's statutes.
FYI, in NH the law that applies to leased tenants is *almost* exclusively related to eviction. I have read through the statues many times and have never found anything that provides a tenant with a legal right to always renew their lease. A lease is a contract and will be read and interpreted in court almost literally to the word in the contract. I know from many personal experiences that if you have in your contract that either party needs to issue notice of a non-renewal within a certain period (usually 30 days but some use 60 days).
But seriously, consider these scenarios as black and white (if your 'bad tenants' are simply just annoyances and you want to get rid of them legally):
1. Your lease with them says it expires 3/31/16 and requires a 30 or 60 day notice to quit (aka written notice of vacating the property and not renewing the lease AND not becoming a tenant at will), read the lease to say something like "notice from either party XX days before the expiration of the lease is required". Send them a notice saying that you will not be renewing their lease and that you need them to vacate the premises by the expiration of their lease, anything beyond the end of their lease is not acceptable and will be considered trespassing. Do NOT give any reason why you are not renewing, you aren't required to.
2. Your lease has an automatic renewal clause but does not say that "either party" can send the notice to quit. Send them a notice that their rent is going up to some absurdly high amount with their renewal. DO NOT USE MARKET VALUE. Why would they move out if you raise it to the median rent? That's just stupid.
3. You can also send them a notice to quit the lease and that if they remain in the property after the lease expires they will be considered a tenant at will and their month-to-month rent will be something like $2,400. There are NO rent control laws in NH, you can raise the rent to any level you want.
In NH, the lease you have is considered a legal contract (obvious right?) and the terms are considered BEFORE the standard landlord tenant laws, unless there is some sort of breach of the contract. If the courts don't uphold the terms of a lease, then what would be the point of making a lease? ;)
Disclaimer: I'm not an attorney, and obviously get legal advice if the terms of you ending your tenants lease is not clear in your lease.
I'll give you a great personal example: I had a lease that expired in June (years ago) and at the beginning of that month my landlord asked if I was renewing my lease. I said, no I had planned on going month-to-month. He said he does not allow month-to-month (tenant at will, these are the same thing in NH) and that I would be required to sign a new lease or I would owe an additional months rent for not giving 32 days notice, and he would keep my security deposit. Now, I had read the lease very carefully and the terms were clear. I was to give 32 days notice if I was vacating the property before the expiration of my lease and would be held financially responsible for the apartment until he found a new tenant or the lease expired. The lease clearly said that if the lease expired I would automatically become a tenant at will in what's called a "holding over period" and that the lease would be month to month, as long as he agreed (which he didn't). So I left before the end of my lease and left it in tenable condition.
It did end up going to court, I sued him to get my security deposit back. I ended up winning double the deposit back plus court costs because:
1. He took more than 30 days to send me a letter stating why he was keeping my security deposit (which is why he owed double the amount back to me) and he kept it for an invalid reason.
2. The judge used our exact lease to make a determination on how the ruling should go.
3. I spoke with 5 different attorneys, all of which stated the samething: in NH the lease is viewed as a contract between consent adults and those terms are considered first. Most landlord law is meant to protect a tenant from being abused, and prevent un-lawful evictions and that is all.
Just follow your lease, and make sure you actually know what your own lease terms are! This guy didn't :)
FYI, I tried settling with him many times prior to going all the way to the judge, he specifically kept saying 'let the judge decide' thinking he was in the right.