N.H. Rev. Stat. Ann. § 614:5

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 who is reasonably suspected of having committed a felony or who is reasonably suspected of driving a motor vehicle or operating a boat while under the influence of intoxicating liquor or a controlled drug. It shall also include the pursuit of a person suspected of having committed a supposed felony, though no felony has actually been committed, if there is reasonable ground for believing that a felony has been committed. Fresh pursuit as used herein shall not necessarily imply instant pursuit, but pursuit without unreasonable delay.