The default rule in Ohio is that every employment relationship is "at-will." This means your employer may terminate you at any time, with or without notice, for any reason as long as that reason is not unlawful. An unlawful reason would include termination due to race, color, national origin, religion, gender, age, disability, etc. You, in turn, may leave your employment at any time, with or without prior notice to your employer.
Unless you had an employment contract, your employment was probably "at-will." Therefore, your employer could have fired you at any time, even if you had reported the incident. Further, termination for failure to report appears to be a lawful reason for termination because it is not based upon any of the above factors.
If you feel you have been wrongfully discriminated against due to one of the factors listed above, you should contact an employment attorney. If not, however, it appears your termination was legal.
Cornetet, Meyer, Rush & Kirzner
No attorney-client relationship implied or accepted without a signed fee agreement. This response is theoretical only and for purposes of discussion. Attorney is not liable for any opinion expressed herein. Attorney is licensed in Ohio only.
The first thing people need to understand about employment law is that most wrongful terminations, even they really were wrongful from the employee's standpoint, are not actionable. That is because Ohio is an employment at-will state. Therefore , unless you are working under an actual employment contract---and most employment situations do not fall in that category---you can be fired or any or no reason, unless it is contrary to public policy. And your employer wrongly blaming you for not filing an incident report would not qualify under the public policy exception.
If you really were fired for something that wasn't your fault, your redress would be to file for unemployment compensation.