Tenant given the lease on 10/1/2011 for 1/1/2012 to 12/31/2012. Its been a month and the tenant refuses to sign the lease. What's are my rights as landlord?
Thank you,

Give them notice that they will have to move at the end of their lease, if there is not a new lease in place.

I will assume your old lease does not have a automatic renewal in it ?

If they stay with no lease the terms of the lease is in effect except that they are now on a month to month basis

If they stay without a lease and the month to month takes effect, I don't have a legal binding document.
Also, I've never knew of an automatic renewal on an old lease. The old lease was for one year, 1/1/2011 to 12/31/2011.

If they stay without a lease and the month to month takes effect, I don't have a legal binding document.
...
Actually, you do. Except that the term will be, beginning with the new year, month-to-month. But other terms still apply.

Assuming you have any normal standard lease, it remains in effect, everything is still binding expect for the date, in this case, the time frame is just month to month, but all other terms and rules of the lease are still valid.

NJ is very tenant friendly in this regard. There are limited reasons that a landlord can use to terminate a tenancy.

You may find this site helpful

LSNJLAW - F: Chapter 5: Ending or Breaking Your Lease (http://www.lsnjlaw.org/english/placeilive/irentmyhome/tenantsrights/chapterfive/)