We consider two-phase fibre-reinforced piezoelectric composites of arbitrary transverse phase geometry wherein both the constitutents and the composite exhibit transverse isotropy. Such a material is described by a total of 10 overall elastic moduli, piezoelectric constants and permittivities. It is shown that five universal relationships which are independent of geometry at given volume fractions connect six of these effective physical constants. The result is a generalization of the relations found by Hill [J. Mech. Phys. Solids 12, 199 (1964)] for the purely elastic case. An additional relationship between three of the other constants is also known to exist.