N.H. Rev. Stat. § 614:9
The term "fresh pursuit" as used in this subdivision shall include fresh pursuit as defined by the common law and also the pursuit of a person who has committed a felony or is reasonably suspected of having committed a felony in this state, or under RSA 614:7, II a person who is reasonably suspected of driving under the influence of intoxicating liquor or controlled drugs, or who has violated any motor vehicle statute, ordinance, or any other law in this state in the presence of the arresting officer referred to in RSA 614:7, or for whom such officer holds a warrant of arrest for any offense. It shall also include the pursuit of a person suspected of having committed a supposed felony in this state, though no felony has actually been committed, if there is reasonable ground for so believing. Fresh pursuit as used herein shall not necessarily imply instant pursuit, but pursuit without unreasonable delay.
RSA 614:9
1941, 34:3. RL 439:9. RSA 614:9. 1995, 193:2, eff. Jan. 1, 1996.