To claim a child as a dependent, the custodial parent does not need Form 8332 or any permission from the noncustodial parent. If you are the custodial parent, just file your tax return and claim the child.
Form 8332 is used when the custodial parent allows the noncustodial parent to claim the child. In order to claim the child, the noncustodial parent needs Form 8332 signed by the custodial parent.
The custodial parent is the parent with whom the child lived for the greater number of nights during the year.