N.H. Rev. Stat. Ann. § 282-A:68

The judicial review provided by RSA 282-A:67 shall be exclusive of all other methods of judicial review of unemployment compensation decisions, including extraordinary writs, including the writ of certiorari. No unemployment compensation decision shall be questioned, invalidated, vacated, set aside, suspended, or otherwise impeached by any court or other tribunal except in accordance with the provisions of this section and RSA 282-A:67.