From AMS Glossary
After U.S. weather observing practice, a ceiling classification applied when the ceiling value is the vertical visibility upward into precipitation.
This is necessary when precipitation obscures the cloud base and prevents a determination of its height. All precipitation ceilings are estimations, but the following are used as guides: the height corresponding to the upper limit of a ceilometer reaction; the top of a ceiling-light projector beam; or the height at which a ceiling balloon or pilot balloon completely disappears. These guides usually indicate values that are lower than the actual vertical visibility. Precipitation ceilings are designated P in aviation weather observations.