Each department is responsible for collecting Safety Data Sheets (SDS) for chemicals in their possession. It is recommended that individual departments also keep a collection of SDS on hand for their chemicals or, at the bare minimum, frequently used chemicals.
To find specific SDS for chemicals, it is recommended that individuals go to the website of the chemical manufacturer, like Sigma-Aldrich, Fisher Scientific, or Avantor, or use an aggregate search sites like the Chemical Safety or SDS Online.