New York’s advertising campaigns promoting the state’s economic-development opportunities have faced criticism for their high costs and meager returns in job creation. Now they have encountered another challenge.

A former North Carolina Supreme Court judge has filed complaints with the U.S. Office of Special Counsel and a New York state ethics panel alleging that taxpayer-funded ads Gov. Andrew Cuomo’s administration has run in North Carolina violated the Hatch Act by interfering with the gubernatorial and legislative races...