Dr. Sandeep Kapoor drew the board's attention after the TMZ.com Web site published information about the prescription for Michelle Chase, which the site said was an alias Smith used, the Los Angeles Times said.
Medical Board spokeswoman Candis Cohen said, "We're reviewing this as we would regarding potential misconduct by any physician" and declined further comment except that the information related to Smith, who died Feb. 8 of unknown causes.
Cohen said the board is looking into, among other things, whether it is illegal for a doctor to prescribe medication to someone using an alias.
TMZ.com posted a document it said was the prescription order issued by Kapoor for Chase. The celebrity Web site also posted a document it claimed was the air bill from the pharmacy to Vicky Marshall in the Bahamas. Smith was born Vickie Lynn Hogan; she married Texas oil tycoon J. Howard Marshall in 1994.