In the fall of 2013, one of Mexico’s top housing officials posted an item on Twitter about an advertising campaign promoting mortgages for low-income Mexicans. The campaign’s message was simple: “The most important thing in life is in your house.”

It carried the tag line, “Homes with value.”

The official, Alejandro Murat Hinojosa, knows something about homes with value, especially across the border.

Over the years, he and members of his immediate family — starting with his father, José Murat Casab, a former governor of Oaxaca — have bought at least six properties in the United States, including two condominiums near a ski resort in Utah, another at the beach in South Texas and at least one in Manhattan, according to records and interviews. In New York, José Murat’s children have also lived for periods of time in one of the more modest condos at the luxurious Time Warner Center overlooking Central Park.

Ownership of the homes was often obscured through variations on family names listed on deeds or through shell companies, according to records examined by The New York Times. In fact, on the day the younger Mr. Murat tweeted about the housing program, public filings in Florida recorded the transfer of a $750,000 Boca Raton condo that had been purchased in his wife’s name to an entity called IMRO 2013 Trust.