We present the results of three searches for correlations between ultra-high energy cosmic ray events (UHECRs) measured by Telescope Array and the Pierre Auger Observatory and high-energy neutrino candidate events from IceCube. Two cross-correlation analyses of UHECRs are done: one with 28 "cascades" from the IceCube 'high-energy starting events' sample and the other one with 12 high-energy "tracks". The angular separation between the arrival directions of neutrinos and UHECRs is scanned. The same events are also used in a separate search stacking the neutrino arrival directions and using a maximum likelihood approach. We assume that UHECR magnetic deflections are inversely proportional to the energy with values 3°, 6° and 9° at 100 EeV to account for the various scenarios of the magnetic field strength and UHECR charges. A similar analysis is performed on stacked UHECR arrival directions and the IceCube 4-year sample of through-going muon-track events that was optimized for neutrino point source searches.