It depends. If your business is covered by the Family and Medical Leave Act (FMLA) and the employee is eligible for leave, you must allow the employee to take up to 12 weeks of leave to care for a new child. This leave is unpaid and must be taken within a year of the child's arrival.
Generally, employers are not required to offer paid leave to either parent after a child's birth. However, if you do offer a paid maternity leave benefit, you must offer this leave to new fathers as well as mothers or risk a lawsuit for sex discrimination. In other words, if you offer paid leave, it must be parental leave, not maternal or paternal leave.
In addition, the states of California and New Jersey, as well as the District of Columbia, now provide paid family leave to new mothers and fathers. (The state of Washington has a similar law, but it has not gone into effect due to budgetary constraints.) Many others states are considering paid family leave laws as well.
For more on this, see Providing Pregnancy and Parental Leave.