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So I sent in my acceptance via snail mail (as was requested) around four weeks ago, and haven't gotten a response yet.

Should I be worried? Should I call recruiting?

Thanks in advance. Sorry for being a neurotic law student..

Just call/email recruiter to confirm that they got your mail. It's perfectly okay to do so if you haven't gotten confirmation yet and wanted to make sure.

I'd call. There's zero downside. They'll either say they received it and look forward to having you next summer, or that they haven't received it and ask you to send another one.

This is what recruiting departments exist for. Just call.