Check out form 8332.

"Claims" and "lives with" don't really relate in the tax regulations. "Claims" for what?

The various credits and dependency qualifications, having custody or not, having physical presence, etc, are all different. And lots of times, the judge's legal statement isn't how the tax rules are read.

A L E R T !!

First time poster, and the link might just be spam.   I wouldn't click on it.

@kkkkks  -  you've been reported as a spammer.

Most of the time what a state divorce-court judge "rules" is in a decree to which the spouses have agreed ("stipulated").  Even if this was a contested case, if the noncustodial parent meets the federal tax law requirements (which aren't much), then the custodial parent would be in contempt of court if he/she disobeyed the judge's order.  And of course in that case, she would go to jail, and the other parent would probably have custody until she agreed to obey the judge and was released.  

IRS Publication 504 covers who may claim a dependency exemption, and how, following a divorce or separation. Regardless of what the custody orders the court has issued, federal law determines your federal tax status. Therefore, the IRS requirements supersede a county or state court order.

As @IRonMaN said. Check out form 8332