Does severance delay my unemployment claim?

My employer is paying severance in instalments and I am not sure whether to file now. I am in Raleigh, in case local advice matters. The agreement mentions a release and a payment schedule. Who should I ask before signing?

Keep everything in writing and save the confirmation numbers. It made the follow-up calls so much easier.

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.