The charges relate to an incident on March 28 when Culliver is alleged to have hit a cyclist before ramming into the vehicle of a witness who was trying to prevent him from leaving.
Culliver entered his not guilty plea at the end of last week in Santa Clara County Superior Court, according to The San Jose Mercury News.
The 25-year-old missed the entire 2013 campaign with a torn ACL and could face stiff competition for a starting role next season with the Niners expected to pick a cornerback in the Draft.
His current contract expires at the end of next season and, although the 49ers have expressed a desire to extend his deal, his arrest could affect proceedings due to a possible league punishment.
Culliver is one of a number of San Francisco players to have found themselves with legal problems recently, including linebacker Aldon Smith, who was arrested on Sunday after allegedly making a false bomb claim at an airport.