N.H. Rev. Stat. Ann. § 423-A:4

The shared valuation shall be assessed in the municipality in which the property is located. It shall be taxed at the rate applicable in that municipality. The tax so assessed shall be collected by the municipality in which the property is located. The share of such tax, as specified in the tax base sharing agreement, shall be remitted within 30 days after collection to the other municipality or municipalities on the basis of the terms of the agreement entered into pursuant to RSA 423-A:2.