Mr Chuwit on Tuesday posted a Facebook message saying sources at the Immigration Police Bureau told him the 28-year-old hit-and-run suspect was due to return from Singapore tonight.
However, Immigration officers could not arrest hm on arrival because no arrest warrant had been issued.
He was still free to travel in and out of the country.
"The attorney general told police that the suspect failed to report when due, but there was an indication of a desire to attempt escape.
Buit it is still the duty of police to seek a warrant for the suspect from the court," Mr Chuvit said.
"Police are not taking any action and allowed a wealthy man's son take a flight to watch an F1 race and return to Thailand as if nothing has happened."
He said the Red Bull heir's hit-and-run case reminded him of an old Thai song "Amnat Khong Ngern" (Power of Money). One of the verses in the song goes, "Cash lets you shop as you please, but you better believe, even the strongest of will can be trampled by the almighty dollar. Oh money, oh money, its power is beyond reach. Respect, friends earn by riches. Without any you’re nothing but an outsider. In truth its just paper made by wretched money makers…who fell slave to the influence of the almighty dollar."
He wrote that if his son was the suspect he would tell his son to respect the law and face the truth.
"The police must not have double standards, one for a rich man's child and another for a poor man's children. The police are walking a thin line without any care about how society feels," Mr Chuwit said.
Pol Maj-Gen Suebsak Pansuri, commander of the Metropolitan Police Division 5, confirmed that Mr Vorayuth is in Singapore and said his lawyer had previously requested a postponement of a scheduled meeting with prosecutors.
He said Attorney-General's Special Litigation Department director-general Seksan Bangsombun had instructed police to investigate the legitimacy of Mr Vorayuth's medical certificate issued by a hospital in Singapore in connection with his lawyer's request -- which allowed him to avoid and beat the statute of limitations of a speeding charge relating to the death of the policeman .
"We've been working with the Immigration police and we'll have to wait for the result of the investigation before taking further action," Pol Maj-Gen Suebsak said.