Our Gemara on amud aleph discusses the propensity of a person to threaten and exaggerate his intentions, and this does not necessarily serve as evidence of his guilt:

With regard to one who takes an ax in his hand and says: I will go and chop down so-and-so’s date-palm tree, and the palm tree is found chopped down and tossed on the ground, we do not say that he chopped it down, but rather we search for evidence.

The Chasam Sofer (Shu”t YD 326) uses this Gemara as a proof that even a person who stated suicidal intent, such as, “I will climb the roof and jump off,” and we saw him climb the roof but did not see him actually jump, is not ruled as a suicide, despite the circumstantial evidence of finding his body at the bottom.

The notion of suicidal threats and evaluating the degree of lethality is one that challenges the mental health profession. Many people say they want to kill themselves, or that they do not want to live, and some may even threaten that they will kill themselves, yet by far not all of them actually do so. Of course, the consequences of not taking a suicide threat seriously are literally life-threatening. Yet if every person who was suicidal was sent to the hospital, there would be no room on the psych wards, and no one who is depressed would ever see a therapist, as they would not want to be committed. While in the end, it is often unpredictable, it is worth understanding some of the risk factors and indicators:  

According to the CDC (https://www.cdc.gov/suicide/risk-factors/index.html):  

Personal factors that contribute to risk are:

 There is a real phenomenon known as suicide contagion and suicide clusters, where, within a community or within a certain time frame across communities but accelerated via media, there is an uptick in suicides. Teens who are impulsive and turn to their peers for setting their behavioral norms are particularly vulnerable to this effect.

A final tricky suicidal warning sign is when a severely depressed person suddenly seems to be happy and in a good mood. This might not be true recovery but rather a sense of relief from having decided to end their life, and, now being at peace, as they make their final plans, a feeling of well-being and tranquility settles over them. This can be devastating to family members and friends, who might have genuinely been happy seeing this person’s newly lifted spirits, only to discover suddenly that the person killed himself. (Simon R, Gutheil TG. Sudden improvement among high-risk suicidal patients: should it be trusted? Psychiatr Serv. 2009 Mar;60(3):387-9.)