Can you request that the umbilical cord and placenta be immediately tossed in the medical waste?

You can, but...: The placenta is sometimes sent to the pathology lab for analysis in certain medical conditions, and is often "re-cycled" to extract hormones, and other valuable substances from it. The hospital where you deliver needs to be made aware of your "request" before delivery.

Yes: However, the umbilical cord and placenta are important cues to fetal health and usually undergoes a pathologic examination and visual inspection by the delivering obstetrician. There are important cues to potential need for newborn studies based on examination and i would encourage you not to have it immediately put into medical waste.

Maybe/not: When you enter a hospital for care you are agreeing to accept their basic healthcare protocols. You have a choice & they do too.If their legal department requires that they hold it for a defined period for potential study, it is unlikely they could or would comply.Delivery care is one of the more litigation sensitive areas of the hospital & specimens removed during procedures are part of that mess