The literature on local public (school) finance has shown that the use of local head taxes to finance schools leads to an effcient allocation of households and pupils to districts (Tiebout, 1956; Hamilton, 1975; Calabrese et al., 2009). This paper revises this well established result, using a two-community model with a housing market that adds two layers of realism to the analysis: not every household receives direct benefits from schools (e.g. some do not have children at school age) and communities are vertically differentiated, in the sense that one of them is exogenously preferred to the other by every household. In such context, head taxation leads to an ineffcient allocation of households to districts, even if local governments set local spending levels effciently given their population. The ineffciency emerges because too many intermediate income "in-school" households reside in the rich district in equilibrium. Income taxation is ineffcient as well but, in a counter-intuitive result, it may cause smaller effciency losses than a lump-sum tax.