The general answer is no. In New York State workers’ compensation is the exclusive recourse for on-the-job injuries. This has been the case for over a hundred years. The concept was to bring immediate cash and medical benefits to injured workers, rather than forcing them to sue for damages (a very lengthy and expensive process). It was a great concept at the time, but what was once a liberally construed and fair system has become ultra conservative, slow and overly complicated.
There are a few exceptions to this general rule. They are:
If your employer was not carrying workers’ compensation insurance (which is required) at the time of your accident.
If a third party (another contractor on a construction site) was responsible for your injuries you may sue that company for pain & suffering while continuing to receive workers’ compensation benefits.
Injuries involving falls from scaffolds. You are permitted to sue general contractors and property owners for elevated falls regardless of the employer’s own negligence or mistake.
Motor vehicle accidents caused by another driver (who is not your co-worker).
If work is being done at your place of business (electrical, plumbing, no ice removal from parking lot, etc), as long as the contractor is not a co-worker, and has it’s own company.
Intentional injuries caused by boss or co-worker. Must be “intentional.” Gross negligence still protects your employer from being sued.
Finally, on a slightly different note, if you ever hire a live-in or domestic worker, nanny, etc. for more than 40 hours per week (or to live in your home) to care for you or your family members you must obtain your own workers’ compensation policy. Your homeowner’s policy will not protect you.