N.J. Stat. § 2A:156-2
The term "fresh pursuit" as used in this chapter shall include fresh pursuit as defined by the common law, and also the pursuit of a person who has committed a high misdemeanor or is reasonably suspected of having committed a high misdemeanor in this state, or who has committed or attempted to commit any criminal offense in this state in the presence of the arresting officer referred to in section 2A:156-1 of this title, or for whom such officer holds a warrant of arrest for a criminal offense. It shall also include the pursuit of a person suspected of having committed a supposed high misdemeanor in this state, though no high misdemeanor 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.
N.J.S. § 2A:156-2