We search for correlations between the positions of extragalactic objects and the arrival directions of ultra-high energy cosmic rays (UHECRs) with primary energy E ≥ 40 EeV as observed by the surface detector array of the Telescope Array (TA) experiment during the first 40 months of operation. We examine several public astronomical object catalogs, including the Veron-Cetty and Veron catalog of active galactic nuclei. We count the number of TA events correlated with objects in each catalog as a function of three parameters: the maximum angular separation between a TA event and an object, the minimum energy of the events, and the maximum redshift of the objects. We determine the combination of these parameters that maximizes the correlations, and we calculate the probability of having the same levels of correlations from an isotropic distribution of UHECR arrival directions. No statistically significant correlations are found when penalties for scanning over the above parameters and for searching in several catalogs are taken into account. © 2013. The American Astronomical Society. All rights reserved. ; 0 ; SCOPUS: ar.j ; info:eu-repo/semantics/published