The park, in Blanding, is the site of an ancient Pueblo Indian ruin, as well as the modern-day museum.
The sculpture is a modern interpretation of a Hopi symbol of a flute player. Made by artist Joe Pachak, it has welcomed visitors to the park for 19 years.
It raised objections only recently from a group of Blanding's more conservative residents, who were concerned that the figure has male anatomy, Paul said.
At first park officials were going to ban the figure from the park altogether. But another group of citizens complained of censorship.
"So, our solution -- I believe we have served everyone the best we possibly can," Paul told The Associated Press on Thursday. "It's not right in the front of the museum on the street, where everyone can see it."
The statue depicts an image commonly found on rock panels in southern Utah, a man believed to be announcing the arrival of spring with a flute.
The flute player is a Hopi clan symbol that's often confused with the ancient fertility god Kokopelli. Tribal elders specifically asked the park to make the distinction clear to visitors, Paul said.
One of those who supported the move, Harold Lyman said he objected to the phallic symbol because it isn't always depicted in traditional rock art images of the flute player. Therefore, he told The Salt Lake Tribune, it's not an essential part of the image.
Susan Dexter was among those who favored leaving the sculpture in place.
"Give me a break. It's not like a massive erection like some of the ones you see on the panels. It's nothing like that," Dexter told the Tribune.
The work is among several pieces of Pachak's sculpture that grace the 17-acre heritage park. The artist didn't return a telephone message left Thursday by the AP at his home in Bluff.
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