According to the site, Singer filed court papers on Tuesday, Jan. 28, one day after sources confirmed to Us Weekly that the two had separated after 27 years of marriage. "It is like war of the roses between them right now," one insider told Us of the couple, who share daughter Avery.
Added another source: "They like to put on appearances like things are okay. It's been going on like this for a while."
In fact, Singer may already be moving on with another man. As previously reported, the reality star, 56, was spotted on a date with a younger guy, Travis Millard, at The General restaurant in New York City last week.
"They were holding each other's hands at one point, and he had his hand on her back as they were walking out," an onlooker told Us. "They were just overall very touchy with each other all throughout dinner."
Singer, for her part, has said little about the split except to thank fans for "all the love & support" on Twitter. "For my daughter's sake, I would appreciate everyone respecting our privacy during this difficult time," she wrote.