Statements from his wife — who survived the crash, along with her husband, 7-year-old daughter and 4-year-old son — and motorists driving behind Patel, along with videos from the tunnel, led San Mateo County prosecutors to file three counts of attempted murder charges Monday against Patel, San Mateo County District Attorney Steve Wagstaffe said. Prosecutors included enhancements for domestic violence and causing great bodily injuries, according to charging documents.

“We do believe the evidence establishes the necessary intent to kill,” Wagstaffe said.

Patel, 40, appeared in a Redwood City courtroom Monday afternoon, but his defense attorney asked for a delay until Feb. 9. Patel, appearing in a holding cell behind a pane of glass, was not visible from the courtroom’s audience as he communicated with his attorney, Josh Bentley.

Judge Jeffrey Finigan granted the delay and the prosecution’s request for no bail and orders that Patel not harass his family.

“I’m not certain he will make it to the microphone,” Bentley told the judge. Patel had been hospitalized for almost a month since the Jan. 2 crash with “serious lower body injuries” until he was released Friday and booked into San Mateo County jail, Wagstaffe said. Patel has not spoken to investigators since the Jan. 2 crash, he said.

Patel’s wife is still hospitalized, Wagstaffe said, and Deputy District Attorney Dominique Davis, who handles domestic violence cases for the office, told the judge she had not been contacted about the stay-away orders. Wagstaffe said after court that the wife’s attorney told prosecutors that she would talk to investigators only “when she was physically ready to do so.”

After she was hoisted by helicopter from the crumpled car earlier this month, she spoke with paramedics, making “incriminating” statements about her husband, Wagstaffe said. Motorists also told investigators they saw no brake lights on the Tesla when it suddenly “made a hard right,” and plunged off the cliff near Devil’s Slide, he said.

The judge granted Davis’ request Monday for no bail citing the “potential danger to family members.”

Wagstaffe said his office was still looking into why Patel drove off the cliff.

“We’re looking into what led up to this. Was there depression or anything else?” Wagstaffe said. “It wasn’t just that he was trying to kill them, he was trying to kill himself too.”

CHP investigators are still examining the car, he said, but so far no problems have been determined.

“Nothing found yet,” Wagstaffe said.

Wagstaffe said the Tesla was not in self-driving mode at the time of the crash and they recovered no videos from the vehicle. All four family members were buckled into their seat belts at the time.

The daughter suffered a serious injury, while the boy escaped with just bruises, Wagstaffe said, calling the family’s survival from the crash “stunning.” The children have been staying with one of Patel’s sisters, he said.

California Highway Patrol officers arrested Patel, a Pasadena radiologist, the day after the crash at Stanford hospital. CHP investigators turned their case over to prosecutors on Jan. 6 and his office has spent more than three weeks firming up their prosecution. Because Patel was hospitalized during that time, investigators had the luxury to take their time on the probe. Once he was transported to San Mateo County jail in Redwood City on Friday and booked, prosecutors had to file charges within two business days.

Firefighters responded to the crash around 10:50 a.m. Jan. 2 and found the crumpled car at the bottom of a steep cliff. Photos of the wreck show the car landed on its wheels and on a dry portion of beach out of reach of crashing waves. Firefighters pulled the two children up the hill and a helicopter rescued the parents.

Patel worked at Providence Holy Cross Medical Center as a doctor of radiology. According to his medical license, he graduated from Wayne State University School of Medicine in 2008.

The L.A. Times reported the Patel family lived on a quiet residential block of single-family homes in Pasadena. Patel would pass out cookies to neighbors. His wife started a mass text thread for neighbors to stay in contact.

Patel’s wife posted photos of her husband and the children on social media — the most recent showing what appears to be her daughter kissing her younger brother on the cheek.

In another post, his wife joked about her husband’s reaction to a proposal on the reality TV show “The Bachelorette.”

“So Dharmy,” someone responded, using a nickname for Patel.

In November 2019, the wife took a selfie with her husband from a pier, the couple smiling into the camera, as the Pacific Ocean rolled beneath them.

Matthias Gafni is a San Francisco Chronicle staff writer. Email: matthias.gafni@sfchronicle.com Twitter: @mgafni