Can I be fired for leaving company property without filing out an accident report and then file a workers compensation claim?

You can file the workers' compensation claim at anytime. Just make sure to notify your employer of the injury and how it happened within 30 days. You have one year to file the claim with the Division of Workers' Compensation.

Regarding termination, there is no protection against that. Some companies have a handbook policy requiring that all injuries be reported immediately. The only prohibition is that they cannot fire you for filing a work comp claim. That is called retaliatory discharge and you can sue them for that. But, if they can blame it on violating a company policy, they will probably get away with it.

In general, you can be fired for any reason or no reason at all. There is an exception if you are fired because you filed a work injury claim. Employers cannot legally fire you for this. As for the accident report, you should notify your employer as soon as possible -- there is usually a quick deadline on this. You have longer to file a workers' compensation claim, but it's best to do so as soon as you can. I always recommend hiring a workers' compensation attorney to guide you through the process and be there in case your benefits are challenged or denied.