You've gotten some good answers. In California I believe it's something called a "5150" where the police can forcibly take you to a hospital to be held for up to 72 hours to assess your risk to yourself – not technically an "arrest" in the criminal sense.
If you're found partway through, depending on your method it's more likely to be paramedics who would be called out. If it's obvious you've attempted suicide, you're likely to be held for at least 72 hours at the hospital, but it's hard to say. Many people are released earlier.