A woman from Hawaii who was reported missing in Los Angeles by her family last month was last seen by US authorities safely crossing the southern US border into Mexico, the Los Angeles Police Department (LAPD) said in an update Monday.

Hannah Kobayashi, 30, was seen on video obtained by US immigration officials crossing on foot into Mexico shortly after she landed in LA from Hawaii and deliberately missed her connecting flight to New York, officials said.

In a news conference, officials said she appeared on the video to be safe and that no foul play is suspected. They described her as a "voluntarily missing person".

The update comes amid a massive search after her family said she sent them cryptic and bizarre messages about her money and identity being stolen.

"The investigation has not uncovered any evidence that Kobayashi is being trafficked or is the victim of foul play," said LAPD Chief Jim McDonnell.

"She is also not a suspect in any criminal activity. Additionally, the investigators noted that before departing Maui, Kobayashi expressed the desire to step away from modern connectivity."

"We’ve basically done everything we can do at this point," the chief added. "She’s left the country and in another nation now."

Ms Kobayashi has been missing since 8 November. She was spotted at several spots around LA in the following days, before vanishing on 12 November.

Her family disputes the police's assertion that she intentionally missed her connecting flight and continue to be concerned for her safety, according to The LA Times.

"The lack of communication surrounding some important details has left us feeling excluded from potentially crucial developments,” her sister, Sydni Kobayashi, said in a statement, according to the Times.

“However, we do remain hopeful and optimistic that the Los Angeles Police Department is doing everything in their power to assist us in locating Hannah.”

On 24 November, Ms Kobayashi's father, who had travelled to California to aid in the search, was reported by police to have taken his own life near the LA airport.

Ryan Kobayashi, 58, was found dead from multiple blunt force traumatic injuries, according to the LA coroner's office.

If you have been affected by any of the issues raised you can visit the BBC's Action Line pages, or contact Samaritans in the UK.

If you're in the US, call 988, or contact Lifeline.