N.H. Rev. Stat. § 273-D:4
No employee in the state classified service shall hold any remunerative elective public office, or have other employment, either of which creates an actual, direct and substantial conflict of interest with the employee's employment, which conflict cannot be alleviated by said employee abstaining from actions directly affecting such classified employment. Determination of such conflict shall be made by the personnel appeals board after the parties are afforded rights to a hearing on the conflict issue. The burden of proof in establishing such a conflict shall be upon the party alleging it. No action affecting said employee shall be taken by the appointing authority because of such public office or other employment until after a full hearing before and approval of such action by the personnel appeals board. If an actual, direct and substantial conflict of interest, which cannot be alleviated by abstention by the employee, is found by the personnel appeals board, the board must approve any action proposed by the appointing authority; and the employee shall be given a reasonable amount of time to leave the employee's public office or other employment or otherwise end the conflict before the appointing authority initiates that action.
RSA 273-D:4