The alleged assault occurred in a San Francisco hotel room early Sunday, after the 49ers' playoff victory over the Green Bay Packers, police said in a written statement.
Crabtree has been interviewed with his attorney present and has co-operated with the probe, the statement said. The receiver hasn't been detained or arrested, and he agreed to be available for more questions in the future.
The probe is being handled by the department's special victims unit. When the investigation is done, the findings will be forwarded to the district attorney's office, which decides if charges should be filed.
Authorities didn't release any further details.
49ers General Manager Trent Baalke said the team is aware of the allegations.
"The 49ers take such matters very seriously," he said in a statement. "We will have no further comment at this time as the legal process is ongoing."
San Francisco is preparing to play the Atlanta Falcons in the NFC championship game on Sunday. The winner goes to the Super Bowl.
The 49ers said Crabtree made the trip to Atlanta. The team referred all other questions about the matter to Crabtree's attorney, who was not immediately identified.
This season, Crabtree became the first San Francisco wide receiver to log more than 1,000 yards in a season since Terrell Owens in 2003. He had a career-best 1,105 yards receiving, including a single-game high 172 yards on eight receptions in a win over Arizona.
In Saturday's NFC division matchup against the Packers, Crabtree caught two touchdown passes and wound up with nine receptions and 119 yards for the Niners (12-4-1).
Associated Press Sports Writer Antonio Gonzalez contributed to this report.
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