First, we don't cover legal stuff here, you should consult a lawyer or request your criminal record to see if you committed a crime. (likely if there is no record, no crime was committed in the official sense)
Filling out the application
For the sake of the question, let's assume you (the OP) got in trouble, your license was suspended, then later reinstated. You also have not been able to verify whether or not you committed a crime.
On your application, this can easily make or break your chances of getting a job...
If you claim no crime but there is one on your record and they do a back ground check, it's almost certain your application is going straight into the trash can.
If you claim no crime and either you have a clean record legally or no check is made, you proceed through the application process as normal.
If you claim a crime but do not have one, you are adding a factor against you. This won't likely disqualify you, but might put you at a disadvantage against other applicants.
What should you do?
First, you really need to know where you stand legally. Was this an infraction? If so, you're good to go; no criminal record! Or was this a misdemeanor? If so, you should continue noting it on applications. Many applications specifically state "excluding minor traffic violations" or similar. If so, you don't need to note your situation.
Second, I would continue to note it on your applications until you are able to confirm whether or not you committed a crime. Otherwise, there is a risk you could get put on "do not hire" lists for saying you aren't a criminal then having a background check flag you as one.