The intervention program allows first-time offenders to have charges against them dismissed after participating in the program and meeting certain conditions. The county prosecutor will decide whether Rice is allowed to enter the program.
If not, prosecutors have offered Rice a plea bargain that would spare him jail time if he participates in anger management counseling.
The former Rutgers star walked to the courthouse holding hands with the woman, who is now his wife. He said he is a "happy father and a happy husband." When asked by reporters what he hoped would happen, Rice responded, "for you all to have a blessed day."
Rice pleaded not guilty to aggravated assault causing serious bodily injury during the Feb. 15 incident at Revel Casino Hotel.
Security video obtained by TMZ Sports shows Rice removing the motionless body of Janay Palmer from the elevator. She did not comment as the two walked into the courthouse.
The couple married a day after Rice was indicted.
Originally, Palmer and Rice were charged with simple assault, but the Atlantic County prosecutor's office reviewed the case and dropped the charge against Palmer.
Copyright 2014 by The Associated Press