New Hampshire's landlord-tenant laws don't specifically prohibit or allow subleases, which means that your specific provisions lie in the terms of your lease. Whether or not you are able to sublease your rental will lie entirely on your lease and your landlord. As always, be sure to obtain written permission from your landlord.
A sublease is an agreement between the original tenant (sublessor or sublandlord) under a lease agreement for a rental unit and a new individual (sublessee or subtenant) who does not have a direct connection with the original lease agreement; the sublease agreement is tied to and incorporates the original (master) lease. In New Hampshire, if the original lease does not contain language giving permission for the tenant to enter into a sublease, the original tenant (sublessor) must obtain written permission from the landlord to do so. The original tenant (sublessor) is still bound by all the requirements/obligations under the original (master) lease agreement.
A New Hampshire sublease agreement should include the following sections: