The concrete memorial in Berlin's Tiergarten park, near the memorial to the Jewish victims of the Holocaust, features a window into which visitors can look and view a video of a same-sex couple kissing.
Police said Monday that security guards reported that overnight the window had been painted over.
Police currently have no suspects and wouldn't say whether there was surveillance video of the crime.
Nazi Germany declared homosexuality an aberration that threatened the German race and sent thousands of gays to concentration camps.
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