The Justice Department is investigating the Consumer Product Safety Commission and its Chairman S. John Byington in connection with the agency's award of two consulting contracts totaling $17,878 to a Los Angeles firm.

A letter sent yesterday from Byington to Assistant Attorney General Barbara Babcock, revealed that an investigation was started last October following publication of a Jack Anderson column which pointed out that the consulting firm, Terzian Associates, did public relations work for Byington on a volunteer basis after Byington hired the firm for government work.

Informed sources told The Washington Post that the FBI has questioned Byington, Carl Terzian, who heads Terzian Associates, and five staff members of the CPSC in the past month.

Two contracts are under investigation. A $9,500 award was made in July 1976, reportedly for the development of training films for community service officers in the 13 regional offices of the CPSC. The films were designed to help the officers "to communicate with the media and the community," according to a CPSC spokesman.

An $8,378 contract signed in September 1976, was to develop a training program so CPSC, state and local officials could make speeches to spread the word on product safety, the spokesman said.

In his letter to Justice, Byington said "Since April of 1977, these same contracts have been extensively scrutinized and reviewed on numerous occasions by our congressional oversight committees, individual senators and congressmen, and have been the subject of considerable attention by the press.

"In addition to making these documents fully available to the requesting parties and public, the commission staff has expended far more time and resources in informing the public about this matter than appears to be warranted from the facts," he added.

Byington also wrote that he feels the "CPSC and I have been subjected to what I believe to be a substantial amount of unfair and unjustified criticism."