The Los Angeles police said this week that they were ending their search for a Hawaii woman whose family had reported that she was missing, after determining that she had traveled alone to Mexico.

The search for the woman, Hannah Kobayashi, 30, had drawn national attention and led to rampant speculation on social media after she flew from Maui to Los Angeles on Nov. 8 but did not board her connecting flight to New York and stopped contacting her family.

On Monday, the Los Angeles police said that video footage showed that, on Nov. 12, Ms. Kobayashi walked alone, with her luggage, across the United States-Mexico border. The police said that there was no evidence of any crime or foul play and that they were classifying her as a “voluntary missing person.”

On Wednesday, Ms. Kobayashi’s family said in a statement issued by a lawyer that they remained concerned about her and that learning she may be in Mexico “has only heightened our fears.”

“The search is far from over, and our family is committed to doing everything possible to bring her home,” the statement said.

Here is what to know about the search for Ms. Kobayashi.

She did not board a connecting flight to New York.

Ms. Kobayashi flew from Maui to Los Angeles International Airport on Nov. 8 and decided for unknown reasons not to board her connecting flight to Kennedy International Airport in New York, the police said.