Spoiler warning: Plot and/or ending details follow.
She was a trader who worked to provide weapons to the white Phaedans and Robert "Bobby" April. In a 2259 visit to Phaedus IV, Mudd met the crew of the USS Enterprise and assisted Nyota Uhura in reaching the planet from orbit. After rescuing a shot-down landing party, Mudd and April returned to the vessel, where April locked out the crew from the ship's systems and the pair took control of the bridge. (TOS comics: "Countdown to Darkness, Number Two", "Countdown to Darkness, Number Three")
Afterwards, April contacted the Klingon commanders on Qo'noS, offering them the Enterprise in exchange for making him governor of Phaedus IV. When he found out how Kirk and Spock were making there way through the jefferies tubes, April had bulkheads activated to seal them off. Scotty managed to disable Protocol 31, and Kirk and Spock subdued April and Mudd before he could hand the Enterprise to Commander Kor. April was placed in Starfleet custody at a starbase, but Marcus and Pike covered up the Phaedus IV incident and Protocol 31, much to Kirk's chagrin. (TOS - Countdown to Darkness comics: "Countdown to Darkness, Number Three", "Countdown to Darkness, Number Four")