N.J. Stat. Ann. § 11A:5-3

Parent and spouse of veteran who has died in service. A parent and spouse of any veteran who died while in service and who would have qualified under this chapter as a veteran, shall be entitled to a disabled veterans' preference. Where both a parent and spouse survive, the exercise of the preference by one shall suspend the right of any other so long as the first individual who exercises preference remains in the employ of the State or any political subdivision operating under the provisions of this title.