If Princess had tour T-shirts, they’d sport the coolest list of venues ever — New York’s Carnegie Hall and Minneapolis’ First Avenue. That’s it. A two-gig tour for this Prince cover band.

“I’m weirdly in denial. My body is in shock. I can’t actually picture that I’m going to be on the First Avenue stage,” said Maya Rudolph, the former “Saturday Night Live” star who is lead singer of Princess. “I keep envisioning the crowd from ‘Purple Rain.’ ”

“It’s surreal,” added Gretchen Lieberum, the other half of Princess. “We’ve both seen ‘Purple Rain’ an embarrassing amount of times.”

Princess’ debut at the film’s centerpiece club is part of the second annual fundraiser staged by former Prince & the Revolution drummer Bobby Z to raise awareness and money for the American Heart Association. He suffered a near-fatal heart attack two years ago.

The duo is honored that he invited them. “He’s making our dream come true,” said Lieberum. Added Rudolph: “I’m going to ask him to adopt us when we get there.”

Princess has done seven or eight gigs so far. Their sound is 1980s Prince — “Controversy,” “Darling Nikki” — with a bit of “Purple Rain” dialogue mixed in. So is their look, with Rudolph in a “Dirty Mind” trench coat and Lieberum in a police cap, à la Prince backup singer Jill Jones.

“I’ve done some research and, over time, there will be brocade with matching brocade boots,” promised Rudolph, who now stars in the NBC sitcom “Up All Night.”

A Princely backup band

Friends since the early 1990s at the University of California, Santa Cruz, where they bonded over their love of Prince, the two have long talked about doing something musical.

Lieberum, who has released four solo albums of jazz-soul, came up with the idea of a Prince project when Rudolph moved back to California after leaving “SNL” in 2007. Pregnancies kept them from pursuing Princess until last September, when they did “Darling Nikki” with the Roots on “Late Night With Jimmy Fallon.” That was followed by a gig in Brooklyn and a few more in Los Angeles.

In Minneapolis, they will be backed by a Purple-tinged band featuring Bobby Z and his former Prince bandmates Dez Dickerson, Dr. Fink and André Cymone. Musicians from Mint Condition and Alexander O’Neal’s group will help out along with Questlove, drummer for the Roots and musical director on “Fallon.”

Questlove is amped.

“I like meeting someone who has the same Purple IQ that I do,” he said in a separate phone interview. “Maya and Gretchen can actually match me note for note. There’s nothing that I can stump them on. I fought hard to sort of make myself Prince’s Billy Preston to their Beatles.”

He is equally excited to play some of the syn-cussion instruments Bobby Z used in concert with Prince.

“I’m drumming for most of it, and Bobby promised I could play some of his percussion patches from his touring days,” said Questlove, who is also playing a DJ set Friday at First Avenue and curating a Prince tribute Thursday at Carnegie Hall. That concert also will feature Princess along with the Roots, Elvis Costello, Bettye LaVette, D’Angelo, DeVotchKa and the Blind Boys of Alabama.

Prince dug Maya’s mom

Rudolph, 40, grew up on Prince music. She collected his 12-inch singles. At 14, she finally saw him in concert.

“Live, that’s an entirely different level of my love and appreciation for what he does. He is music. You can feel that,” said Rudolph, daughter of the late R&B singer Minnie Riperton and producer Dick Rudolph. “Gretchen and I went to see the last tour together [in 2011] and I was pregnanter than pregnant, and he was unbelievable. His music is part of my history. ”

She met Prince in 2005 when he performed on “SNL.” At the end of the night, she went up to shake his hand. “I thought: ‘God, he has no idea of who I am. I’m so embarrassed.’ I was trying with every fiber in my body to savor the moment and not geek out and say something stupid. Then at the end of the conversation, he said, ‘I really loved your mom.’ I was really surprised that he knew the connection. And really moved.”

The next day they found themselves on the same airplane to L.A. “I got to talk to him on the flight and introduce him to my daughter, who was only 4½ months old then. It was pretty magical,” said Rudolph. “He’s very lovely.”

She and Lieberum, who are known to break into “Purple Rain” dialogue at any moment, are overjoyed about their Purple Pilgrimage — though purifying themselves in Lake Minnetonka seems out of the question in March.

“That’s OK, I’m not good with cold water,” said Rudolph.

Countered Lieberum: “I’m going to go do it anyway.”

First Avenue is the main attraction. Rudolph didn’t make it to the club when she was in the Twin Cities filming “A Prairie Home Companion” in 2005.

Lieberum was disappointed to learn that the backstage scenes in Prince’s movie were actually filmed elsewhere.

“After we performed ‘Purple Rain,’ we were going to run angrily through the halls,” Lieberum said.

“She was,” Rudolph clarified. “One of us had to stand in the hallway and cry like Jill Jones. And I’m not blond.”