A call to your accountant would be in your best interest to find out about the tax and/or double tax. I do believe, however, you will be taxed by both New York and New Jersey.
As far as the homestead rebate program, "The Homestead Rebate Program provides rebates for homeowners and tenants who occupied their principal residence in New Jersey on October 1, paid property taxes on that dwelling either directly or through rent, and whose gross income for the entire year does not exceed certain limits."
The cutoff date has always been October 1 so assuming for 2009 it stays October 1 then if you were neither a NJ homeowner nor a tenant on October 1, 2009, you will not be eligible for the 2009 homestead rebate. Here is a link for the 2008 rebate program: http://www.state.nj.us/treasury/taxation/homestead/nonsenior
Hope that information helps about the homestead rebate program. Keep in mind that last year the State reduced the gross income limits so many people who qualified years before, did not qualify last year because their income was above the maximum allowance...unfortunately, I was one of the people who got cut from receiving the rebate.
I hope all goes well with your move and I hope you enjoy living in Bloomfield. I grew up in the neighboring town of Belleville but my husband is from Bloomfield and my in-laws still live there.
Gina Chirico, Sales Associate
Prudential New Jersey Properties
973-992-6363 ext 116