City Manager Jamie Davidson told The Daily Herald of Provo that courts have ruled in similar cases that such displays are not illegal.
"People may find things in society objectionable that may not be illegal," Davidson said.
The decision came after Cox filed a complaint with the Orem Department of Public Safety.
Cox spent $567 on Feb. 15 to buy the 19 T-shirts, saying the images on the clothing were offensive to the community's standards. She says she plans to return them later, toward the end of the chain store's 60-day return period.
The shirts cost about $28 each on the website for PacSun, which sells beach clothes for teenagers and young adults.
Though charges were not filed against the store, Cox said she's glad she spoke up for standards in her community.
Cox said young women need to understand that their beauty and worth should not be based on highly sexualized images in the media.
"This message needs to be shared with our young girls everywhere," she said. "It was for these children and youth I made a stand."
The City Council will be briefed on legal grounds for the decision when it meets Tuesday.
City code prohibits anyone from putting "explicit sexual material" on public display. The city defines that as "any material that appeals to a prurient interest in sex and depicts nudity, actual or simulated sexual conduct, sexual excitement, or sadomasochistic abuse."