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We present the most sensitive and extensive survey yet performed of extragalactic H₂CO 6 cm (4.829 GHz) emission/absorption. Sixty-two sources were observed with the C-band system of the Arecibo Telescope to a 1 σ rms noise level of ∼0.3 mJy. We report a new detection of H₂CO 6 cm absorption toward NGC 520 and the confirmation of H₂CO 6 cm absorption toward several sources. We report confirmation of H₂CO 6 cm emission toward the OH megamasers Arp 220, IC 860, and IRAS 15107+0724. At present these are the only extragalactic H₂CO 6 cm emitters independently confirmed. A characterization of the properties of formaldehyde absorbers and emitters based on infrared properties of the galaxies is discussed. We also conducted a simultaneous survey of the H110α hydrogen recombination line toward a sample of 53 objects. We report the detection of H110α toward the giant extragalactic H II region NGC 604 in M33.