Kerri F. Dunn's car was vandalized and covered with racist, anti-Semitic and sexist epithets on March 9, while she spoke at a forum on racism.
The incident prompted faculty to cancel classes and students to stage rallies the following day.
Two witnesses interviewed by police investigators allegedly saw Dunn, a visiting professor of psychology at Claremont McKenna College, commit the vandalism, police said in a statement.
Dunn also gave inconsistent statements during two interviews conducted jointly by the Claremont Police Department and the FBI, said police Lt. Stan Van Horn.
Police will forward their findings to the district attorney's office, Van Horn said. One charge that could result, he said, is a misdemeanor count of filing a false police report.
The witnesses, he said, were of college age and friends of a student at Claremont McKenna College.
The Los Angeles Times reported that Dunn was "enraged" by the police assertions.
"This is like a very big deal if they think I'm a suspect," Dunn told the newspaper. "I didn't want any of this from the beginning. This is so overshadowing the bigger problem on campus, which is that the administration has turned its head regularly on hate speech and hate crimes."
The Times also quoted police sources as saying that Dunn initially claimed $1,700 worth of property, including a CD player and a briefcase, had been stolen from her car, but later told investigators the items had turned up.
The alleged hate crime was seen as the latest in a rash of recent hate incidents, including the burning of an oversized crossed used in an art project at Harvey Mudd College and the writing of a racial epithet on a calendar picturing George Washington Carver at Claremont McKenna College.
The new allegations stunned students and faculty in this college community known for its rigorous academics.
"We've taken our second stab in the back at a time when we thought we were secure," said Marc Bathgate, 21, president-elect of the Claremont McKenna student government.
Others worried the allegations, if proven true, would overshadow last week's demonstrations in support of diversity and tolerance.
"My fear ... is that people will say 'see they're blowing this all out of proportion. There are no real incidents of racism,'" said Sidney Lemelle, associate professor of history and black studies at Pomona College.
Claremont McKenna College will conduct its own investigation of Dunn, whose two-year contract lasts through June, said college President Pamela Gann. The school's faculty will convene Thursday to discuss the police department claims, she said.
The consortium of seven independent institutions includes undergraduate colleges Claremont McKenna College, Harvey Mudd College, Pitzer College, Pomona College and Scripps College, as well as the Claremont Graduate University and the Keck Graduate Institute of Applied Life Sciences.
Claremont is about 30 miles east of downtown Los Angeles.