The scope of the investigation into the improper handling of drug samples by a state crime lab chemist spans 34,000 cases over the past nine and a half years, according to the Patrick administration, heightening fears that the breach of justice could be widespread and difficult to unravel.

Public safety officials on Wednesday said they had distributed a list of samples compiled from the former Department of Public Health drug lab database to the state’s district attorneys, United States Attorney Carmen Ortiz and the Committee for Public Counsel Services for review.