I realize that your question has not been answered for months and now it is probably way too late because your baby has probably already been born by now. Anyway... Here is what my experience is with cord blood.
With my first son I told the nurse in the delivery room that we wanted to collect the cord blood. She responded with "oh. You want to do that" in a very negative tone. I think she just really didn't want to do the extra work to collect the blood. She then left the room and came back with a cord blood collection kit. They took the cord blood and sent it to cardinal glennon hospital in st. Louis (st. Louis is where my kid was born). This was donated to their research program at cardinal glennon. I would have liked to have it stored and frozen for the future but I never could get all the information on how to do this.
With my second son, he was premature by 5 weeks. Due to the complication that the premature birth caused, it was not an option to collect the cord blood because all hands were on the baby and no one could care less about the cord blood. Sounds understandable to me!
So, your hospital may have cord blood collection kits on the delivery room floor. They may not. You could actually go to the delivery floor of the hospital and ask one of the nurses if they stock cord blood collection kits and how to get them. I bet that would be your best source of information as they are the actuall ones that do the collection.
Hope this helps.