The New Jersey Constitution of 1947 (Annotated) Art. V, § I, ¶ 3

3. No member of Congress or person holding any office or position, of profit, under this State or the United States shall be Governor or Lieutenant Governor. If the Governor or Lieutenant Governor or person administering the office of Governor shall accept any other office or position, of profit, under this State or the United States, the office of Governor or Lieutenant Governor, as the case may be, shall thereby be vacated. No Governor or Lieutenant Governor shall be elected by the Legislature to any office during the term for which the person shall have been elected Governor or Lieutenant Governor.