I know that there are certified TCAS/autopilot/FD systems (380 comes to mind), but the normal modality that I am familiar with is where TCAS alerts are provided to the pilot, who then decides what action to take.
As for the rules on the certified systems, I cannot comment, but I am sure that information is obtainable.
Of course, one can imagine one avoidance maneuver triggering more avoidance maneuvers, and a cascade of paperwork at ATC. So the rules and use cases are likely heavily vetted.
To generally answer your question, the most common TCAS implementations do not couple with AP or FD, and rely on pilot decision making to further avoid conflict.
Addendum #1 The A380 does apparently have an integrated AP/FD mode that works with TCAS. I don't know the rules and the certification criteria and goals, but here is an article on it. http://www.airbus.com/newsroom/press-releases/en/2009/08/easa-certifies-new-autopilot-flight-director-tcas-mode-for-a380.html