When Lily Tomlin comes onstage, you can never be sure who’s going to show up. It could be Edith Ann, the uninhibited girl with indelible insight into adults. It could be Sister Boogie Woman, a Gospel Groove evangelist who complained about having no shoes until she met a man with no rhythm. It could be Trudy, the beloved bag lady and social theorist at the heart of Tomlin’s Tony Award-winning, one-woman show “The Search for Signs of Intelligent Life in the Universe.”

These characters, and more, showed up with Tomlin in Orono on Friday, when she was featured in the culminating event for Women’s Week at the University of Maine. Playing to a full and charged-up house at the Maine Center for the Arts, Tomlin swept up the audience with the intrepid wit and deft perspective of her stand-up routine.

The evening included excerpts from monologues she has developed in more than 30 years of being one of the country’s leading comics. Some pieces dated back to her early comedy routines and to her days in the early 1970s on the TV show “Laugh-In.” She drew heavily from “The Search,” which was written by her artistic partner Jane Wagner and performed on Broadway in 1986, with a revival in 2000.

For some, Tomlin’s touring show may pull too much from past work, but even if the bits were ones that fans have seen multiple times, it was more like a visit from an old friend than hearing jokes to which you already know the punch lines. That, in part, accounts for her two Tony Awards, five Emmys, a Grammy and a hefty handful of other prestigious theater awards.

Tomlin’s well-established cosmic worries – as simple as: if olive oil comes from olives, and peanut oil comes from peanuts, where does baby oil come from? – still manage to be funny. And even when the routine doesn’t fly because she trips on her lines, Tomlin employs enough self-effacement to win the support and good will of the audience. “Reality,” Trudy told us a long time ago, “is nothing more than a collective hunch.”

After 40 years in the biz, Tomlin, 63, could run the risk of being outdated and stale as an entertainer. But she doesn’t seem to grow old, whether she appears on “Murphy Brown,” “Magic School Bus” or “West Wing” (in which she is currently playing a recurring role as the president’s secretary). Her originality, mixed with qualities of Lucille Ball and Mark Twain, keep pushing up against any number of hunches, such as: “Why is it that when we talk to God, we’re praying, but when God talks to us, we’re schizophrenic?”

You can’t help wondering about – and perhaps longing for – a world in which she actually is the secretary to the president of the United States. What would she do if she were? “Put a tack on his chair,” she said.