N.J. Stat. Ann. § 18A:38-9

Any child living remote from any public school in the district in which he resides shall be allowed to attend a public school in an adjoining district, with the written consent of the county superintendent or county superintendents of each county in which the districts are situate. One copy of such written consent shall be filed with the secretary of the board of education of the district in which the child resides and one copy thereof shall be filed with the secretary of the board of education of the district in which such child shall attend school.