Hope this helps.
Licensed in Indiana & Illinois
Since it looks like you are asking about Indiana taxes, the answer in a very plain way would be no. You have to wait it out for a year sometimes two. You will file your tax exemptions with in six weeks after moving in and then they will take into effect on your 2010 tax bill and once the lender redoes your escrow. One point I have to make is any overage in 2011 you pay will be returned to you at the end of the year. Hope this helps.
Your lender will have to underwrite the mortgage based on the most recent yearly tax bill(s), however if you know the taxes are going to be less you can request them to escrow less $$ at closing and monthly. You will probably have to sign an affidavit at closing stating that you are responsible for any shortfalls in escrow should the taxes come out higher than expected.
You may also want ask your Realtor to find out if there is a cutoff date for filing to obtain the lower tax rate for the year. In some areas you have to be the owner of record on Jan 1st to qualify. Some areas have no cutoff too. You'll definitely want to find this out.
Hope this helps!
Don't count on property taxes going down especially in Cook County. Assessed values may be going down, but the multiplier used will be going up. Chicago has a budget that they need to maintain. Lowering taxes isn't something that is going to happen across the board.
Once you own the property, you may be able to protest your taxes and get the tax reduced but again the multiplier is going to go up to bring taxes back where they were.