(Measure passed House, amended, in lieu of H.R. 6358) Federal Railroad Safety Authorization Act - Requires that the comprehensive safety report required to be filed with Congress by March 1976, under the Federal Railroad Safety Act, contain a description of regulations and handling criteria, established as of June 30, 1975, applicable to the transportation of radioactive materials by railroad, together with the projections of the volume of such materials to be transported by railroad through 1980. Authorizes appropriations to carry out the provisions of the Federal Railroad Safety Act through September 30, 1976. Authorizes appropriations for the purposes of the Hazardous Materials Transportation Act of $7,000,000 for fiscal year 1976 and $1,750,000 for the transition period through September 1976.