In Colorado, the relevant standard is that the person "appears to have a mental illness and, as a result of such mental illness, appears to be an imminent danger to others or to self or appears to be gravely disabled." Colorado Revised Statutes § 27-65-101 et seq.
The standard is very similar in Florida where the applicable statute is called the Baker Act a.k.a. the Florida Mental Health Act (s. 394.463, F.S. Ch. 65E-5.280, FAC, statutory language available here), although it is worded slightly differently:
A person may be taken to a receiving facility for involuntary
examination if the following three criteria are met:
There is reason to believe that he or she is mentally ill. This means an impairment of the mental or emotional processes that exercise
conscious control of one’s actions or of the ability to perceive or
understand reality, which impairment substantially interferes with a
person’s ability to meet the ordinary demands of living, regardless of
etiology. For the purposes of this part, the term does not include
retardation or developmental disability as defined in Chapter 393,
intoxication, or conditions manifested only by antisocial behavior or
substance abuse impairment.
Because of his or her mental illness the person has refused voluntary examination or is unable to determine whether examination is
necessary;
and
- Without care or treatment, the person is likely to suffer from neglect resulting in real and present threat of substantial harm that
can’t be avoided through the help of others; or there is substantial
likelihood that without care or treatment the person will cause
serious bodily harm to self or others in the near future, as evidenced
by recent behavior.
Whether, in light of all of the facts and circumstances, a particular person meets that standard would typically be a question of fact for a court reviewing the decision in hindsight to determine, with considerable deference given to the person who mades the call.
Given the extreme consequences of a "false negative" that does not led to commitment and results in a death or serious injury, relative to the consequences of a "false positive" which leads to an unnecessary several days of commitment in a mental health facility, judges tend to give a person making a marginal call to commit a person the benefit of the doubt.