A Hawaii woman who vanished after landing in Los Angeles three weeks ago disappeared voluntarily as she sought to “step away from modern connectivity” and was last seen crossing into Mexico, police said at a news conference.

Hannah Kobayashi, 30, appeared unharmed as she walked alone with her luggage into a tunnel at the San Ysidro crossing about 125 miles (201km) south-east of Los Angeles around noon on 12 November the day after her family reported her missing, LA police said Monday. Authorities made the discovery after reviewing surveillance video from the US Customs and Border Protection late on Sunday.

The Los Angeles police chief, Jim McDonnell, said there was no evidence Kobayashi was being trafficked or was otherwise a victim of a crime. Investigators conducted “extensive” witness interviews and reviewed video surveillance but have found no evidence of foul play. Kobayashi’s disappearance is now classified as a “voluntary missing person”.

“We’ve basically done everything we can do at this point. She’s left the country and in another nation now,” he said, adding that if she returned to the US, law enforcement would be notified.

McDonnell said Kobayashi had a right to her privacy, but urged her to reach out to her family or law enforcement.

“A simple message could reassure those who care about her,” McDonnell said. He explained that the missing person case would remain active until her safety was confirmed by law enforcement.

Kobayashi went missing after the budding photographer from Maui did not make a connecting flight to New York on 8 November to travel for a new job and to visit relatives. She told her family she would sleep in the Los Angeles international airport that night.

Family members assumed she was on standby for another flight, according to her aunt, Larie Pidgeon. The next day, Kobayashi texted them to say she was sightseeing in Los Angeles, planning to visit The Grove shopping mall and downtown LA, Pidgeon said.

On 11 November the family received “strange and cryptic, just alarming” text messages from her phone that referenced her being “intercepted” as she got on a Metro train and being scared that someone might be stealing her identity, her aunt said. Her disappearance set off an extensive search and attracted significant media attention.

Her father, Ryan Kobayashi, who had been in the search party along with volunteers, was found dead by apparent suicide on Sunday 24 November in a parking lot near LA international airport, police and her family said.

McDonnell said during a police commission meeting last Tuesday that detectives determined Hannah Kobayashi missed her connecting flight intentionally. Kobayashi’s sister, Sydni Kobayashi, disputed his statement in a social media post.

Police said on Monday that after Hannah Kobayashi was seen in various locations around LA, she requested that her luggage, which had been checked to New York, be sent back to LAX. She then returned to the airport to retrieve it on 11 November and did not have her phone when she left again, according to police.

Investigators found that she had “expressed the desire to step away from modern connectivity”.

Police also identified and questioned a man that Kobayashi was seen with on the Metro. He was “cooperative” and said he met her at LAX, police said.

Sydni Kobayashi did not immediately respond to an emailed request for comment. Members of the public who were in the “Help Us Find Hannah” Facebook group, which garnered the interest of more than 25,000 participants, shared a post from the group on Monday that said the family would be shutting the group down after “threats against their lives and the lives of their small children”.

The post also said Sydni Kobayashi and her mother would not be responding to any messages.

The Los Angeles police department said in a statement that it would not continue the investigation into Mexico but encouraged her to contact police or the US embassy so that officials can “confirm her wellbeing”.

During the news conference, McDonnell reflected on all that the family had endured these last few weeks.

“My ask would be to anybody considering doing this, think about the people you’re leaving behind, your loved ones who are going to be worried sick about you,” he said.