2 month old dropped from 87th-95th percentile for height to 15th. has remained 50th percentile for weight, why such a drop in height?

Longer at birth: Many baby's lengths are erroneously "long" at birth because of the stretching out of their heads and molding of the head during the last weeks of pregnancy and during hte birth process. I've had kids whose heads were so molded their lengths changed over an inch by a month of age. I would keep a close eye on the length over the next 2-4 months, and if keeps dropping, then look into it.

Measurement error: Length in infants is a difficult measurement to replicate. Baby's length is dependent upon how tense/relaxed he is. Think how he pulls his legs up when he cries. If 1st length was while asleep and 2nd while awake and resisting, he'll appear shorter. Staff may fail to fully stretch legs, head may move from starting point. Discuss with dr, but unlikely to be a concern.