Joseph and Summer McStay disappeared with their two young sons in February 2010. Joseph was 40 at the time; Summer was 43. Their boys were 3 and 4 years old at the time.
Investigators found rotten eggs on the kitchen counter of their Fallbrook home and two bowls of popcorn in the living room, as well as the two family dogs in the back yard when they searched the residence 11 days after they were last seen. There were no signs of a struggle and no arrangements had been made to care for the dogs.
Surveillance video shows a group of four people that investigators believe is the family walking across the border into Tijuana, Mexico, four days after they disappeared.
San Diego County Sheriff's investigators said Wednesday they believe the people in the video are the McStays, who appeared to have voluntarily crossed into Mexico with no signs of distress.
The U.S. Customs and Border Protection video doesn't show anyone seeking help and there were no signs of forced entry at the McStay home, about 70 miles north of the border, or in their SUV parked near the border. That has led investigators to believe they went to Mexico voluntarily, sheriff's Lt. Glenn Giannantonio said. The family's SUV was towed from a border parking lot
"The reasons behind it? Your guess is as good as mine," Giannantonio said. "It's very odd. We really have no idea what happened to them."
But the Sheriff's Department said it was turning over the case over to the FBI because of that agency's extensive experience working outside the United States.
Investigators phoned relatives Tuesday shortly before the department issued a statement that said the family likely went to Mexico "of their own free will."
Giannantonio said tens of thousands of dollars left in business bank accounts have not been claimed. Joseph ran a business from home designing and installing water fountains.
On the day the family was last heard from, Joseph made his last known phone call to an employee to follow up on a business meeting earlier that day.
Four days later, their SUV was towed from a parking lot steps from the border that has a two-hour limit and is closely watched by guards. Investigators found a Pottery Barn Kids refrigerator and sink for a playhouse, with children's videos like "Franklin Goes to School" inside.
"We simply want to know what happened to our missing loved ones," a statement from the McStays' extended family said. "We are grateful that there has been so much love and support the past 3 years."
The Associated Press contributed to this report.