The 34-year-old man followed a Lawndale Road resident in his Ford pickup through the gate of her private property around 9 a.m. Saturday, Sonoma police Lt. Bret Sackett said.
The man told the woman her animals looked sad and she should make them happy. The woman said his speech was normal but he was not making any sense, Sackett said.
The man abandoned his vehicle and then walked into the park, and responding deputies determined it was registered to a Sacramento resident, Sackett said.
The man's family members said he was despondent over marital problems and in a note he left, he said he was going to visit family in New York, according to Sackett.
The man had not answered his phone or contacted friends, and he is considered at-risk because he is distraught, Sackett said.
Search and rescue teams from Marin, Alameda and Contra Costa counties and state and Sonoma County park rangers searched for the man until early Sunday morning.
The missing man is 6 feet 6 inches tall, weighs about 185 pounds and has brown hair and blue eyes. He was last seen wearing a T-shirt, blue jeans, black and orange athletic shoes, a tan, heavy, canvas jacket and possibly a baseball cap.
The man is not known to be dangerous or to carry weapons, according to the sheriff's office.
Sackett said deputies spoke to many of the estimated 1,500 hikers and horse and bicycle riders in the park Sunday but no one reported seeing the man.
Anyone with information about the man is asked to call the sheriff's office at (707) 565-2650.