Can I claim my 2 boys on my tax return?

According to my divorce papers, my ex is to claim the boys on his taxes because he pays support. I have full custody and they live with me 12 months a year 24-7. The first year after the divorce at tax time I was called to go to H & R Block to sign a paper stating that the boys father can claim them on his taxes. I was told that it didn't matter what was in the divorce papers since I had full custody, he had to have proof that he could claim them with my signature. Now since he doesn't have a paper signed by me for this tax year, does that mean that I can claim them on my taxes. Please let me know, I've about have my taxes electronically completed.
I live in Preble County, Ohio.

I am not a lawyer and not a CPA.

I am from Montgomery county Ohio!!

There is a way for BOTH of you to sort of claim them. I would advise against you claiming them as actual dependants since your divorce decree says otherwise. Yes, it is good for your ex to have your signature stating that he can claim them, but if you did otherwise he could come back at you with some serious legal implications.

What I would do is allow him to claim them for the dependancy spot, but you can claim Head of Houshold. Claiming this status gives you a little extra tax break. Another option would be for you to make a deal with the ex that each of you claims one. . .one is better than none. I hope that you can come to some sort of agreement.