I found out that my Sigma 50 1.4 and Sigma 50-150 HSM II (non-OS)
cannot autofocus in live view with the D600. I have not tested with
other Sigma lenses (sold the 10-20 I had) but I suggest you check to
see if your Sigma lens will work with the D600. I understand there are
problems with Sigma's compatibility with the D800 and possibly the
D7000 as well.
Anyway, it appears newer copies of Sigma lenses are able to autofocus,
and there is a procedure for updating the lenses to allow
autofocusing. However, Sigma didn't want to fix mine unless I could
show them a copy of a receipt showing it was bought in the last 5
years. Even then they won't commit to fixing it unless you send your
lens in first. So you might send it there with a receipt and they
might still refuse to fix it. Terrible product support....!