Severance and unemployment, do they overlap?

I was offered severance of 3 weeks after being let go as a sales associate and I am unsure how it affects benefits. The agreement mentions a release and a payment schedule. Who should I ask before signing?

Rules differ by state. I called the claims line and asked directly, then wrote down the answer and the date.

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