N.J. Stat. Ann. § 52:28-35

Article I. Criminal process issued under the authority of the state of New Jersey against any person accused of an offense committed upon the soil of said state, or upon the eastern half of said Delaware river, or committed on board of any vessel being under the exclusive jurisdiction of that state, and also civil process issued under the authority of the state of New Jersey against any person domiciled in that state, or against property taken out of that state to evade the laws thereof, may be served upon any portion of the Delaware river between said states from low-water mark on the New Jersey shore to low-water mark on the Delaware shore, except upon Reedy and Pea Patch islands, unless said person or property shall be on board a vessel aground upon or fastened to the shore of the state of Delaware, or the shores of said islands, or fastened to a wharf adjoining thereto, or unless such person shall be under arrest or such property shall be under seizure by virtue of process or authority of the state of Delaware.