Am I responsible for taxes due on a bank owned property before closing date?

First time homebuyer, please HELP! My offer got accepted with the expected closing date of 1/05/10. I checked the San Bernardino County website and it shows there are taxes due on the property with installment 1 due on 12/10/09 and the other for April of 2010. Am I responsible for the tax due in December? I should only be responsible for any taxes after closing date, correct?