N.H. Rev. Stat. Ann. § 614:1-a

The provisions of RSA 614 shall not authorize members of state, county or local peace units from other states to pursue persons driving or suspected of driving a motor vehicle or operating or suspected of operating a boat under the influence of intoxicating liquor or a controlled drug into New Hampshire unless the state of origin of such peace unit accords reciprocal authority to pursue such persons to members of duly authorized New Hampshire state, county or local peace units.