N.H. Rev. Stat. Ann. § 530:9

In case a levy is begun upon the property of an inhabitant or nonresident, other than one of the selectmen or of the school board or commissioners, the superior court, upon application of the person whose property is so levied upon, or upon the application of any other property owner in the town or district, shall issue a writ of mandamus ordering the selectmen to assess and collect a tax sufficient to pay the amount of the execution and costs.