N.H. Rev. Stat. Ann. § 654:37-a

If the supervisors of the checklist learn of the death of a voter but do not receive notice as outlined in RSA 654:37, they shall mail to the last known address of the voter a 30-day letter specifically for updating the checklist upon the death of a voter. Such letter shall include the contact information for the supervisors of the checklist to which a response may be sent. If there is no response within 30 days, the supervisors will remove that voter's name from the checklist. If there is a response confirming the death within 30 days, the supervisors may remove the voter's name upon receipt of the confirmation of death.