The Independent Police Complaints Commission (IPCC) has been asked to investigate evidence that Sir Norman, who was an assistant chief constable at the time, asked for a report to be prepared on a witness who was due to give evidence to the inquiry.
The Police and Crime Commissioner Mark Burns-Williamson said the concerns were based on three documents that had come to light following a search ordered by current chief constable Mark Gilmore.
Mr Burns-Williamson said: “This may suggest an attempt to intervene in the course of a public inquiry and influence the manner in which the testimony of a witness, who was due to present evidence before it, was received. I have today referred this to the Independent Police Complaints Commission.
“This is a matter which needs to be thoroughly investigated, and if wrongdoing is demonstrated those responsible must face the consequences of their actions.”
The Stephen Lawrence Inquiry was set up in 1997 to examine the police’s investigation into the London teenager’s murder and failure to secure convictions. Its damning report described the Metropolitan Police as “institutionally racist”.
The allegations against Sir Norman relate to a hearing the inquiry held in Bradford in 1998 as it gathered evidence from different parts of the country.
Sir Norman, who stood down as chief constable last year, is already facing an IPCC investigation over his actions relating to the Hillsborough disaster while serving with South Yorkshire Police.
Derbyshire Police are also looking into allegations he was involved in the attempted sale of stolen platinum during his time as a South Yorkshire officer.