The sheriff said child protection authorities had been notified about the case, although the three Heene children, ages 6, 8 and 10, have not been taken from their parents. The local authorities have also asked federal officials to look into the case.

The sheriff said his conclusions were based on separate interviews of the Heenes and their three children, as well as on searches of their computers, e-mail records and documents in their home. He said the decision to release the balloon and tell the authorities that Falcon was aboard was made two weeks ago.

“These people wanted to get some national attention, with the ultimate hope that they would end up with some form of a TV deal,” said the Larimer County undersheriff, Ernie Hudson.

The Heenes did not comment on the sheriff’s accusations on Sunday, but when Mr. Heene was approached by a reporter for The Associated Press at a Wal-Mart on Sunday morning, he said with tears edging his eyes, “This thing has become so convoluted.” In earlier interviews, he had vigorously denied that the episode was a hoax.

Wittingly or not, the Heenes produced an astonishing reality show on Thursday. Their report of a missing child  first made in the father’s phone call to a local TV station, then followed up by the mother’s seemingly panicked phone call to 911  captured the country’s collective attention as news helicopters tracked the balloon’s ride across northern Colorado.

Family members told the authorities that Falcon’s brother Bradford had claimed he saw the 37-pound boy in the compartment when the balloon accidentally broke off its moorings. Televised by cable news for more than an hour, the wayward balloon was found to be empty when it came to a landing, prompting fears that Falcon had fallen out. Hours later, it was discovered that he had been home the whole time, hiding in an attic above the garage.