Lead halide perovskite nanocrystals, which offer rich photochemistry, have the potential to capture photons over a wide range of the visible and infrared spectrum for photocatalytic, optoelectronic, and photon conversion applications. Energy transfer from the perovskite nanocrystal to an acceptor dye in the form of a triplet or singlet state offers additional opportunities to tune the properties of the semiconductor-dye hybrid and extend excited-state lifetimes. We have now successfully established the key factors that dictate triplet energy transfer between excited CsPbI3 and surface-bound rhodamine dyes using absorption and emission spectroscopies. The pendant groups on the acceptor dyes influence surface binding to the nanocrystals, which in turn dictate the energy transfer kinetics, as well as the efficiency of energy transfer. Of the three rhodamine dyes investigated (rhodamine B, rhodamine B isothiocyanate, and rose Bengal), the CsPbI3-rose Bengal hybrid with the strongest binding showed the highest triplet energy transfer efficiency (96%) with a rate constant of 1 × 109 s-1. This triplet energy transfer rate constant is nearly 2 orders of magnitude slower than the singlet energy transfer observed for the pure-bromide CsPbBr3-rose Bengal hybrid (1.1 × 1011 s-1). Intriguingly, although the single-halide CsPbBr3 and CsPbI3 nanocrystals selectively populate singlet and triplet excited states of rose Bengal, respectively, the mixed halide perovskites were able to generate a mixture of both singlet and triplet excited states. By tuning the bromide/iodide ratio and thus bandgap energy in CsPb(Br1-xIx)3 compositions, the percentage of singlets vs triplets delivered to the acceptor dye was systematically tuned from 0 to 100%. The excited-state properties of halide perovskite-molecular hybrids discussed here provide new ways to modulate singlet and triplet energy transfer in semiconductor-molecular dye hybrids through acceptor functionalization and donor bandgap engineering.