"My dad used to say, 'there are no happily ever afters--only new battles.'""
- – Neeoma
Connally worked as the union representative for the Docker's Guild on Babylon 5 in 2258. Severely shorthanded and forced to work with substandard equipment, the workers endured a series of serious accidents, culminating in the death of one of them, Alberto Delvientos. Connally was approached by Jeffrey Sinclair and Michael Garibaldi, but they were unable to resolve it. When the Senate refused to allocate any more funding, Connally helped organize a "blue flu." In response, the Senate sent Orin Zento to negotiate with her, with negative results. That night, the workers staged a full scale, illegal strike. In their next meeting in the morning, Zento invoked the Rush Act and Connally prepared herself with the rest of the workers for security teams to arrest them. After the security teams went in, Garibaldi eventually brought Connally out, but Sinclair had another idea. Connally watched with pleasure as Sinclair used his new authority under the Act to give the workers what they wanted.
In 2259, Babylon 5 was forced to host 25,000 Earthforce troops on short notice, which caused several delays in the station's docking schedule. Connally registered a complaint to Commander Ivanova about the long hours her workers had to put in to get their operations back on schedule, and Captain Sheridan responded by authorizing paid time-off for the workers later.
Miss Connally did not appear in the episodes Strange Relations or GROPOS, but was directly mentioned by other characters so it can be assumed she occupied the same position from 2258 until 2262 at least.