A psychiatric profile was a record kept as part of an individual's personnel file.
In 2266, Spock reported that deceased lieutenant junior grade Joe Tormolen record included a psychiatric file. (TOS: "The Naked Time")
In 2371, Quark downloaded Kira Nerys' psychiatric profile from Deep Space 9's computers as part of his plan to create a realistic hologram of her for Tiron. (DS9: "Meridian")