Whether you should run a criminal reference check on a new hire prior to extending a job offer depends on whether you have a job related reason for doing so.
For example, if the employee is working with cash or with vulnerable persons you may want to perform background checks. Also ensure that relevant laws and regulations in your jurisdiction allow such a check to be performed.
As always, document your procedure and be sure your policy is defensible and not used only for select employee groups to avoid human right complaints.