We report a measurement of KLL dielectronic recombination in charge states from Kr+34 through Kr+28 in order to investigate the contribution of the Breit interaction for a wide range of resonant states. Highly charged Kr ions were produced in an electron-beam ion trap, while the electron-ion collision energy was scanned over a range of dielectronic recombination resonances. The subsequent Kα x rays were recorded both along and perpendicular to the electron-beam axis, which allowed the observation of the influence of the Breit interaction on the angular distribution of the x rays. Experimental results are in good agreement with distorted-wave calculations. We demonstrate, both theoretically and experimentally, that there is a strong state-selective influence of the Breit interaction that can be traced back to the angular and radial properties of the wave functions in the dielectronic capture.