A man carrying a home-made sword and what looked like a blood-stained chainsaw was allowed into the US from Canada, the Associated Press reports.
Mr Despres also had a knife, a hatchet and brass knuckles
The news agency says Gregory Despres' weapons were confiscated, before US custom officials in Calais, Maine, let him cross the border on 25 April.
The next day he became a murder suspect after bodies of his two neighbours were found in his hometown in Canada.
Mr Despres, 22, was arrested on 27 April and is now awaiting extradition.
The bodies of Mr Despres' neighbours were discovered in the town of Minto, New Brunswick.
The decapitated body of Frederick Fulton was found on the kitchen floor in his house. The man's head was under a kitchen table.
His common-law wife was discovered stabbed in a bedroom.
AP quoted Bill Anthony, a spokesman for US Customs and Border Protection, as saying the Canadian-born Mr Despres was questioned for about two hours before being allowed to enter the country.
Mr Anthony said Mr Despres could not be detained because he was a naturalised US citizen and was not wanted on any criminal charges on the day in question.
"Nobody asked us to detain him," the spokesman said.
"Being bizarre is not a reason to keep somebody out of this country or lock them up... We are governed by laws and regulations, and he did not violate any regulations".
Mr Anthony added that officials in Calais did not have a forensic laboratory.
"They can't look at a chainsaw and decide if it's blood or rust or red paint," he said.
Mr Despres was detained, after police spotted him wandering down a motorway in a sweat shirt with red and brown stains.