Police spokesman Barry Bowling said a report was filed Sept. 20 and that the matter is still under investigation. Spillman hasn't been arrested or charged.
According to a source, Spillman, who was signed by the Cowboys on Aug. 31, has cooperated fully in the investigation.
NFL spokesman Greg Aiello said Thursday the league has been "looking into the matter and will continue to do so."
Police say the incident occurred at the Gaylord Hotel on Sept. 20, the day before the Cowboys played at St. Louis. The team flew to St. Louis later that Saturday, and Spillman played against the Rams.
There was no immediate response from the Cowboys. Spillman's agent, Ron Slavin, and attorney Bruce Ashworth declined to comment to The Associated Press.
Several Cowboys players stay at the Gaylord Hotel until they find apartments, which is the case with Spillman, who signed with the Cowboys on Aug. 31.
Recently, Cowboys coach Jason Garrett addressed the team about off-the-field conduct and mentioned domestic violence as part of his discussion.
On Monday, the team welcomed the return of defensive tackle Josh Brent to the team. Brent was convicted of intoxication manslaughter resulting in the death of his best friend and Cowboys practice squad player Jerry Brown.
Brent spent five months in jail and 45 days in a rehab facility before he was released. He was suspended for the first 10 weeks of the season, but after the league failed to hear his appeal, it was amended. Although he still can't play in a game until Week 10, he's now allowed to work out and take part in meetings with the Cowboys.
"Again, part of what our jobs are as coaches is to create the right environment for our players to function both on and off the field," Garrett said. "So we need to be clear about where we are, we need to be clear that we have a structure in place to help anybody who has any off-the-field issues. Me as a coach, position coaches, player programs, departments, we have a lot of resources here to help guys.
"So that was the first message -- if you're dealing with anything off the field and we can help with, we're here for you. Having said that, there is standards that we have about all off-the-field behavior, and certainly domestic violence applies to that. We're just very clear with how we're going to handle things."
Last week, attorney Gloria Allred alluded to an alleged sexual assault involving an NFL player without naming the player or team.
On Wednesday, Allred had sent a letter to Jeff Pash, the NFL's executive vice president and general counsel, regarding a case she is involved with. When contacted by ESPN, Allred refused to confirm or deny whether it was the Spillman case.
After Allred's initial allegations became public, Pash asked to speak with Allred. In the letter, Allred said Pash invited her client to be interviewed by NFL investigators "on a confidential and appropriate basis."
Allred's letter raised concern about the type of interview her client might have with league officials.
"The fact that you chose to make public your requests to interview our client confidentially causes us concern about whether the interview itself would be kept confidential or tweeted out by you as you did with your letter to me," Allred's letter to Pash said. "However, I am willing to meet with you to discuss your request and also to learn the answers to our important questions posed in my original letter to you (which was not shared with the press)."
Information from The Associated Press was used in this report.