The existence of either horizontal fiscal externalities, in which changes in one jurisdiction's policies affect the government budget of other jurisdictions and therefore the utility of its residents or externalities, in which changes in one level of government's policies affect the budget of another level of government, may lead to non-optimal government policies. These fiscal externalities, then, suggest the possibility of corrective policies. The focus here is on vertical externalities. In a growing literature, these externalities are associated with the extent that tax bases are shared or co-occupied by two different levels of government. Given that co-occupancy is the cause of or at least exacerbates the externality, I consider, the optimal assignment of the tax base and, more specifically, whether the co-occupancy of tax bases is desirable. Specifically, I examine the optimal extent of the tax base of a lower level of government (local) and a higher level (state) in a hierarchical system of governments. The co-occupancy of the tax base influences the magnitude and possible the direction of fiscal externalities associated with the taxes of one or both of the levels of government. Using a model in which there is a continuum of commodities, each with the same demand characteristics, I formally consider whether, as has been asserted in a number of studies, whether it is optimal to eliminate all co-occupancy between the tax bases of the two levels of government. While I find that it is indeed not optimal to have co-occupancy in the tax base in the absence of other corrective policies for the fiscal externality, eliminating co-occupancy does not, in general, eliminate fiscal externalities, meaning that tax rates can still be above or now below the socially-optimal level. Thus elimination of co-occupancy in the tax base is not a substitute for a policy such as intergovernmental matching grants which directly eliminates fiscal externalities. If alternative policies are available such as matching grants that do eliminate fiscal externalities and governments are restricted to set the same tax rate on all commodities in their base, the optimal division of the tax base changes dramatically -- optimality requires both governments tax the entire base. (JEL H77 - Intergovernmental Relations; Federalism)