To explore the hypothesis that KIC 8462852's aperiodic dimming is caused by artificial megastructures in orbit (Wright et al. 2015), rather than a natural cause such as cometary fragments in a highly elliptical orbit (Marengo et al. 2015), we searched for electromagnetic signals from KIC 8462852 indicative of extraterrestrial intelligence. The primary observations were in the visible optical regime using the Boquete Optical SETI Observatory in Panama. In addition, as a preparatory exercise for the possible future detection of a candidate signal (Heidmann 1991), three of six observing runs simultaneously searched radio frequencies at the Allen Telescope Array in California. No periodic optical signals greater than 67 photons/m 2 within a time frame of 25 ns were seen. This limit corresponds to isotropic optical pulses of 8 10 22 joules. If, however, any inhabitants of KIC 8462852 were targeting our solar system (Shostak & Villard 2004), the required energy would be reduced greatly. The limits on narrowband radio signals were 180 -300 Jy Hz at 1 and 8 GHz, respectively, corresponding to a transmitter with an effective isotropic radiated power of 4 10 15 W (and 7 10 15 W) at the distance of KIC 8462852. While these powers requirements are high, even modest targeting could -just as for optical signals -lower these numbers substantially.