Baker has been charged with identity of theft and obtaining property by false pretenses, The Charlotte Observer reported Wednesday.
Zarha's stepmother Elisa Baker is facing second-degree murder charges in the death of the 10-year-old whose remains were found several weeks after Adam Baker reported her missing in October.
The new charges against Adam Baker date to last July when the Bakers moved from Caldwell County to Hickory, N.C., and applied for electrical service from Duke Energy, police said.
He also faces a number of charges in Caldwell County, authorities said, including writing bad checks and communicating threats.
Baker, from Australia, has surrendered his passport and will not be permitted to leave the United States until the legal cases against him are settled, police said.