You can review the information provided by Labor and Industries at http://www.lni.wa.gov/WorkplaceRights/Wages/PayReq/PersonnelRec/default.asp .
If you are employed in WA, your employer likely is regulated by L&I. The major exceptions are employers that are the federal government or tribal governments.
In WA, employees have the right to reasonable inspection of their employment records. However, the law does not specify that an employer must make copies for the employee. So, while an employee has the right to look at the records, the employee has no inherent right to a copy of the records.
For certain jobs, things belong to the employee even if the employer paid for the things. For example, the notary seal and certificate of being a notary belongs to the notary public, even if the notary is employed by someone else. Upon leaving, the notary can take the seal and certificate, even if the employer had paid for the seal to be made and the licensing fees. You can check whether the same rule apply to your job.
You can also contact the place that issued your certificate to find out how you can get a replacement copy. This may end up being the simplest solution.
If the certificate held by your former employer is an original, you likely can go to court to get an order for the employer to return your property.
You should review your specific facts with your attorney to find out your legal options.