There are special rules for determining who gets the exemptions in the case of divorced parents. A custodial parent (1) having custody for the greater portion of the calendar year may claim an exemption if (2) the child received more than half its support from it parents, (3) the parents are divorced or legally separated under a decree of divorce or separate maintenance, are separated pursuant to a written agreement, or lived apart for the last six months of the calendar year, and (4) the child is in fact in the custody of one or both parents for more than half the year. (Section 152(e)).
Notice there are 4 factors in determining if the special rules apply. In your case, if your child lived with each of you for exactly ½ of the year, neither of you had custody for the greater portion of the year and therefore, the special rules do not apply. In that case, the one who contributed most to the support of the child would be entitled to the exemption.
For rules for determining who paid the most support see IRS Publication 17, Your Federal Income Tax, which you can download for free at the IRS site at:
http://www.irs.ustreas.gov/forms_pubs/index.html