If you remove or damage any political advertising on any property that is not yours, you might have to pay a fine of up to $1,000.
It’s not nice, and it’s not worth it.
Here is the law:
TITLE LXIII
ELECTIONS
CHAPTER 664
POLITICAL EXPENDITURES AND CONTRIBUTIONS
General Provisions
Section 664:17
664:17 Placement and Removal of Political Advertising.
No person shall remove, deface, or knowingly destroy any political advertising which is placed on or affixed to public property or any private property except for removal by the owner of the property, persons authorized by the owner of the property, or a law enforcement officer removing improper advertising.
Section 664:21
664:21 Penalty.
VI. (a) Whoever violates any of the provisions of RSA 664:16-a or the provisions of RSA 664:17 relative to removing, defacing, or destroying political advertising on private property shall be subject to a civil penalty not to exceed $1,000.
http://www.gencourt.state.nh.us/rsa/html/lxiii/664/664-mrg.htm