She had been in custody on US$2000 bail until a judge released her at a hearing on Wednesday and scheduled another hearing in three weeks, according the public defender's office.
In addition to the suspicious card, authorities determined that the travel information she provided listed she would be staying at a Waikiki Holiday Inn but didn't include a reservation number and return flight information, court documents said.
An assistant manager at the hotel confirmed to Lau that she didn't have a reservation. Lau said in the court document that he tried to call the number she listed, but her voicemail was full. He said he emailed her and didn't get a response.
Lau said he searched for her on Facebook and found a photo showing a "distinctive tattoo on her left hip area."
The tattoo helped authorities find Mrozak at a Southwest Airlines counter when she was trying to leave Honolulu on August 28, the court document said.
She showed her ID and vaccination card to Lau, who informed her she was being arrested for falsifying vaccination documents.
Other visitors to Hawaii have been arrested for fake vaccination cards, including a father and son from California, who appeared in court via Zoom on Wednesday and waived their rights to a jury trial.