First of all, even though your question pertains to a criminal case and its possible impact on your job qualifications, it is not a Criminal Defense matter. You would probably get more informed responses by reposting this to the "Licensing" Practice Area. The particulars of how that out-of-state case was disposed of could have an impact on its effects. Was a diversionary program like PA's ARD utilized or is it a straight-up conviction? Alternatively you might consider contacting the Civil Service Commission for an opinion. Perhaps others who respond here will have the benefit of past specific experience with such a situation. Good luck.
It can't hurt to apply for the civil service job. If the job involves driving and your license was suspended in PA as a result of the conviction or the charge it's more likely to effect your ability to get the job.