Brian Laundrie, the person of interest in Gabby Petito's death, has been missing since mid-September.
A police spokesman told NewsNation there was "a lot of oddness" in Laundrie's parents' story.
He said authorities were trying to figure out how Laundrie escaped while under surveillance.
Authorities searching for Brian Laundrie in Florida said there were inconsistencies and "oddness" in his parents' story.
"What the family has told us is that he drove out to the park and walked out into the woods," Josh Taylor, a spokesman for the North Port Police Department, told NewsNation last week.
"I don't necessarily know what to believe anymore," Taylor added. "I think it's certainly possible that they're expressing what they know, but we'll see. I mean, this is an ongoing investigation that will continue to evolve."
The interviewer mentioned reports that Laundrie drove his Mustang to the reserve and that his parents drove it back.
"We've said from the beginning there's a lot of oddness here, a lot of things that just didn't make sense," Taylor said.
"I mean, your son walks out there - now they're saying on a Monday, you know, to report that on a Friday, and then be confused on what day that was," he added. "I mean, there are a lot of things that are odd there."
Laundrie's parents last week changed their story about which day Laundrie left, saying he'd vanished a day earlier than they'd previously told the police.
Taylor said Laundrie's father had been helping the FBI search for his son, adding that this could be a sign that his parents were trying to help investigators.
Taylor told NewsNation that authorities so far hadn't found anything related to Laundrie.
He added that "no investigation is perfect" and that the police were "working to figure out" how Laundrie managed to leave undetected during the investigation.
Taylor previously told Insider that Laundrie was under surveillance when he vanished.
Petito, 22, went missing on a "van life" cross-country road trip with Laundrie. The couple set out on July 2, and Laundrie returned home to Florida on September 1 without Petito.
Petito's family reported her missing on September 11. She was found dead on September 19 at a remote campsite in Wyoming.
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