Does severance delay my unemployment claim? (update)

I signed a severance agreement and I am worried about how to report it. There are 15 people counting on me, so I am trying to be careful. The agreement mentions a release and a payment schedule. Who should I ask before signing?

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.

Some states only count certain kinds of severance. A local workforce centre could tell me which.