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Your tenant is not exactly correct in what the law provides, but you can't just put her possessions to the curb.
A law in New Hampshire requires a former landlord to store all tenant property left behind for 7 DAYS from their last day in the apartment. This law gives them the right to go back and get their property during this 7-day period. This law also gives the landlord the right to get rid of the tenant's property without notice to the tenant AFTER the 7-day limit expires.
This law is called RSA 540-A:3,VII:
". . . a landlord shall maintain and exercise reasonable care in the storage of the personal property of a tenant who has vacated the premises, either voluntarily or by eviction, for a period of 7 days after the date upon which such tenant has vacated. During this period, the tenant shall be allowed to recover personal property without payment of rent or storage fees. After the 7-day limit has expired, such personal property may be disposed of by the landlord without notice to the tenant."
Now, the tenant had no right to change the locks. When she left, she gave up possession of the home, so you can enter the premises. But, you cannot simply put the possessions to the curb. You can put the items in storage somewhere, but you must exercise "reasonable care" in doing so. “Reasonable care” can mean leaving the property where the left it inside the apartment, or a former landlord can move your items to a proper storage facility. But a former landlord does NOT have the right to throw away the property; give the property away; damage the property; leave the property outside where it’s exposed to the weather; or carelessly handle the property throughout the 7-day period after their last day in the apartment. The tenant has the obligation to contact you within this 7 day period to arrange a time that is convenient to both of you to pick up their property.
As to the unpaid rent and fees, you can use her security deposit (if you took one) towards that (as well as the cost of hiring a locksmith to get back into the house). If the security deposit doesn't cover everything, or if you never took one, you can sue your tenant in small claims court for the remainder owed. You may only get an noncollectable judgment in the end out of it, but it is an option for you.
If you need clarification or additional information, please reply, and I'll be happy to assist you further. Thank you.