In 2268, she was ordered to accompany a landing party to Arret, though she did not know who issued the order. While there, she witnessed Captain Kirk become inhabited by one of the planet's non-corporeal natives. She became alarmed when Kirk's vital signs became dangerously elevated.
Initially skeptical about the idea of being inhabited herself, Mulhall accused the non-corporeal beings of wanting to steal their bodies. She also suggested that Kirk's easy acceptance of the possibility might have been due to false euphoria, rather than actual interest. She did find the idea intriguing from a scientific perspective.
Mulhall ultimately allowed the energy being Thalassa to occupy her body while Thalassa's husband, Sargon, and their former enemy, Henoch, occupied the bodies of Kirk and Spock, respectively. This was done in order to construct androids in which her consciousness and those of the other entities could be housed permanently. During this process, Thalassa almost refused to give Mulhall's body back, but ultimately did so. (TOS: "Return to Tomorrow")
Background information Edit
Ann Mulhall was played by Diana Muldaur. Her name was spelled in the final draft of the script (dated 15 November 1967) as "Anne Mulhall", but the "e" was dropped in the episode's end credits. According to the same script, "Anne is an attractive woman, about thirty, an astro-biologist."
The character has the distinction of being the highest-ranking female Starfleet character shown in TOS. Though her doctorate was presumably in a science department, Mulhall wore the red uniform of the operations division.
Mulhall was also presumably a relatively new transfer aboard the Enterprise, judging from Kirk's comment to her when she appeared in the transporter room, "Who are you?"