The LASD’s Special Victims Bureau began investigating that case in December 2017.
Spacey is also under investigation for alleged sex crimes in London, according to the Los Angeles Times.
London’s Metropolitan Police would not identify Spacey by name when reached by CNN previously.
The flood of allegations against Spacey began after actor Anthony Rapp shared his own story in an interview with Buzzfeed in October 2017.
Rapp, now 46, said Spacey made a sexual advance toward him in 1986 when he was only 14. Spacey was then 26.
In response to the allegations, Spacey tweeted that he was “beyond horrified to hear [Rapp’s] story,” adding that he did not remember the encounter.
“But if I did behave then as he describes, I owe him the sincerest apology for what would have been deeply inappropriate drunken behavior, and I am sorry for the feelings he describes having carried with him all these years.”
Days later, members of the “House of Cards” production staff detailed sexual harassment and an alleged instance of sexual assault to CNN.
Netflix cut ties with Spacey as a result of the allegations, a move the streaming service says cost them roughly $39 million.
A former TV news anchor later came forward with an allegation that Spacey sexually assaulted her son in 2016.
In London, an investigation commissioned by officials at The Old Vic Theatre, where Spacey served as artistic director from 2004-15, unearthed 20 allegations of inappropriate behavior by Spacey.
The Old Vic said the allegations spanned from 1995 to 2013, with most of the claims taking place before 2009. The theater said at the time that it had not been possible to verify any of the allegations.
Spacey has been silent since putting out his first statement regarding Rapp’s allegations, after which he sought unspecified treatment.
CNN’s Cheri Mossburg and Sarah Moon contributed to this report.