Martin Ventura, a KFC employee, said in a criminal complaint that Koffi Mbairamadji, 46, chased a woman into the restaurant Friday and was then punched by another customer who tried to protect the woman, KOAT-TV, Albuquerque, reported.
Ventura said he believes that's why the man later returned to allegedly break the windows.
The complaint said Mbairamadji allegedly used his wrists to throw a rock the size of a volleyball through a window and then tossed a brick through the drive-through window, KOAT reported.
"All this glass is all over, and it's like, 'What the heck happened?'" Ventura said.
During his arraignment Monday, Mbairamadji said through a translator he was brought to the United States by the United Nations two years ago. There are limited details about who he is or where he's from, KOAT said.
Police said there were no injuries in the incident.
2014: NFL Cheerleaders [PHOTOS]
Ex-Navy SEAL probed over bin Laden revelations