Object with elevation of top

It happens I have a dataset of towers with elevation of top. How can this data be tagged, since object height is missing?

the top of the tower is marked by elevation over sea level?

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If the case is as you say, i.e., the dataset of towers contain elevation of top from the sea level, you can subtract the elevation of the terrain and get the object height
Basically, Object Height (Tower) = Elevation of Top - Elevation of Terrain

Note: Don’t forget the units you are working in.

Please, consider the DEM limited precision (usually horizontal samples are 30+ meters). In other words, if I have accurate data only for the top, is it possible to tag it without referencing the whole object geometry?