Police told the Palestinian Authority news agency that Josey Hollis, who is safe and well, saw his mother disappear under the waves during their boat trip on Wednesday.
There is no evidence to suggest that Rivera, 33, left Lake Piru, said Ventura County Sheriff’s Office sergeant Kevin Donoghue.
He was speaking in response to an online petition, which drew close to 25,000 signatures, requesting that the research be extended beyond the lake.
Sgt Donoghue said, “Our first day was a rescue effort, it was a rescue effort.
“We searched with people on the ground, on the shore. We weren’t just looking for her physically, we were looking for clues, evidence that suggested she had landed.
“We found no clues, no evidence to suggest that it had landed. The most conclusive evidence that we really care about right now is the statements of her son, the only witness.
“He watched his mother disappear underwater. We are therefore very confident that it is in the water and that at some point we will recover it from the lake. ”
Josey was found asleep and alone on the boat while wearing a life jacket. An adult-size life jacket was also found on board.
Sgt Donoghue added, “If we thought for a moment that she might be on earth somewhere, if we had other clues or corroborating information leading us in that direction, we would and we would be there at look and watch. ”
Rivera, best known for playing a high school cheerleader in the musical series Glee, is believed to have drowned at Lake Piru – a popular spot for swimmers about 90 km northwest of central Los Angeles.
CCTV from the platform shows his rented boat leaving at around 1 p.m. and was then found drifting in the northern area of the lake around 4 p.m.
Side-scan sonar systems, which are towed along the water by boats, have scanned the bottom of the lake for objects that resemble a human body.