Which of the following is a key sign that may indicate an inmate’s deteriorating mental state?

Withdrawal from social interactions is a significant sign that may indicate an inmate's deteriorating mental state. When individuals, especially in a structured environment like a jail or prison, begin to isolate themselves from others, it can suggest that they are experiencing emotional distress or mental health challenges. Social withdrawal is often associated with various mental health conditions, such as depression or anxiety, which can worsen an individual's overall well-being.

The other signs listed, while they can also be indicative of certain emotional states, do not carry the same weight in terms of a clear warning signal. Persistent laughter may suggest a coping mechanism or a response to stress rather than a clear indication of mental deterioration. Incessant talking could signify a manic episode or excitement but might not necessarily indicate a decline in mental health. Excessive eating at times can be a reaction to stress or boredom but does not inherently signify a deterioration in mental state. Thus, withdrawal from social interactions stands out as a more direct and concerning indicator of an inmate's mental health decline.