The short answer is yes: the Fair Credit Reporting Act (FCRA) requires you to get permission from your applicant or employee before conducting a background check. Aside from this legal requirement, telling applicants what to expect as part of the selection process is considered a professional courtesy, especially if you’ll conduct background checks, which dig into history that may not be directly related to the work they will be doing.
The FCRA has pretty specific notice requirements. For example, you also need to provide the applicant or employee a summary of their FCRA rights and the appropriate adverse action letters if you decide not to hire them (or terminate an existing employee) because of the background check.
Employers should also keep in mind antidiscrimination protections. Specifically, using criminal histories as a screening tool can have a disparate impact on race and national origin. Because of this, employers should only eliminate applicants based on their criminal history if doing so is job related and consistent with business necessity.