Here are two links to letters from OSHA regarding footwear. I cannot find anything that requires closed shoes in a lab. If there is a reasonable likelihood of exposure, then the employer must provide shoe covers. It states that shoes that are also worn outside the lab are not considered PPE. Each employer must determine what is appropriate footwear based on hazards. http://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=INTERPRETATIONS&p_id=25497 http://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=INTERPRETATIONS&p_id=25439