This may not be as easy as you believe.
The Army usually just does not allow a Soldier to take leave.
Depending on the type of unit they may have block leave and Soldiers can usually only take leave during this time.
However, if it is an emergency there is such a thing called emergency leave that the Soldier can take.
If the unit does not have a lot going on and the Soldier is not necessarily required at his/her place of duty then the Commander can authorize leave.
It all depends on the situation and specifics associated with the issues. You can find all the procedures concerning Army leave and pass policies in Army Regulation (AR) AR 600-8-10. Here is the link to the regulation: http://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/r600_8_10.pdf