There is no exact answer. Im sure they will check you in ER first to determine if you are dialated and contracting enough to be admitted to L&D and always contact your doctor if any sign of labor.
Actually if your water has broken and it's not your first pregnancy they should take you to L&D immediately. My experience back when I was a paramedic most hospitals don't want to deliver a baby in the ER as the infection risks to both the mother and newborn are greater there and leave the hospital open for law suits even if you're uninsured.
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