Maternity leave

I’m due may 17th and I plan to take the maternity leave April 30th. But I realize I will be already 37 weeks so may be the baby will be here that week (or later but I don’t want to take any risks). We don’t have much space so we haven’t really unpacked anything because I will need to move my desk so that the crib will fit in my bedroom (we will move in our new apartment july 1st). So I’m really wondering if I should take the leave three weeks before my due date or maybe the chances that baby comes at 37 are low for first time moms??