Connie is currently single status and has not been in a relationship with any man. She was previously married to an actor, Fabio Sartor in 1988.
Unfortunately, they both divorced in 1994. Even so, she had been married to a Metallica drummer, Dane Lars Ulrich in 2004.
Her marriage gave birth to two boys named Bryce Thadeus Ulrich-Nielsen, and Sebastian Sartor. Unfortunately, their household life did not last long. They decided to get divorced in 2012.