The person can be committed for evaluation. Depending on when this happens. The person might have to remain inpatient over a weekend or holiday. The police have procedures they have to follow. They are not going to take her to a psychiatrist's office. Each area has a facility they take people to when they threaten to harm themselves. Police usually lean to the side of caution. Someone who does not want help. Can lie and say they said it for attention, to make a point. It is up to responding officers and their supervisor. Police would rather take the person to a facility and the person not need psychiatric help. Than not take them and they harm themselves. This is a dangerous game for anyone to play.