How does one determine whether a chemical requires hazardous waste disposal?
You may find information from the US Federal government relating to this questions at the following sites:
https://www.epa.gov/hwgenerators/steps-complying-regulations-hazardous-waste
https://www.epa.gov/rcra/resource-conservation-and-recovery-act-rcra-regulations

Furthermore, your organization (theoretically) has a local waste discharge permit that it must adhere to as well. If chemical waste is not common where you work, you or the responsible party should review the permit requirements and the operations taking place.