Chris Watts claims that his wife strangled his daughters, but police believe that his story doesn't add up

Under police questioning not long after his pregnant wife and young daughters vanished from their Colorado home earlier this month, Chris Watts allegedly admitted he strangled his spouse, Shanann Watts — but he gave a startling reason for doing so.

According to an arrest affidavit obtained by PEOPLE, Chris allegedly said that after he told Shanann, 34, he wanted to separate, he saw her strangling their 3-year-old, Celeste, while their 4-year-old, Bella, lay “blue” and apparently lifeless nearby.

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In response, Chris allegedly claimed, he “went into a rage” and strangled Shanann.

But authorities aren’t buying his shocking explanation. On Aug. 15, two days after Shanann and the girls were reported missing and hours before the announcement that their bodies had been found on the property of Chris’ former employer, he was arrested.

The 33-year-old faces charges of first-degree murder in all three deaths, among other charges.

A source close to the investigation tells PEOPLE that Chris’ alleged defense is not plausible.

“There is absolutely no evidence that she killed her children,” the source tells PEOPLE in this week’s issue. “None at all. And there is physical evidence to tie him to their murders. Strangulation is a very personal way to kill someone, with a lot of physical contact. Just based on the preliminary evidence, everything is consistent with him killing them all.”

• For more on the shocking killings of Shanann Watts and her two young daughters, subscribe now to PEOPLE or pick up this week’s issue, on newsstands Friday.

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Image zoom Shanann Watts (right) and her daughters Shanann Watts /Facebook

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Investigators allege Chris was having an affair with a co-worker before murdering his family.

Prior to his arrest, Chris gave stilted TV interviews on his front porch pleading for his family’s safe return. “He didn’t seem upset at all,” observed neighbor Terry Witt at the time.

Causes of death in the three killings have not been confirmed and police have not discussed a motive — though, in charging Chris with murder, they dismissed his account of what happened.

“We’ve just begun our investigation in many ways,” the investigation source tells PEOPLE, “but we have a lot of evidence that points straight to Chris.”

He has not entered a plea and his attorney did not respond to PEOPLE’s requests for comment.