We used Arecibo Observatory and the Green Bank Telescope to observe OH in twelve early-type galaxies with known reservoirs of dense gas. We present three new detections of OH in absorption in the 1667 MHz line. One objective of our survey was to find evidence of molecular outflows, but our sensitivity, and the strength of the OH absorption, were insufficient to detect outflows. The detected sources have infrared luminosities and dust temperatures among the lowest of any galaxy detected in OH absorption. The ratio $L_{rm HCN} / L_{rm CO}$, a measure of the dense gas fraction in galaxies, is a powerful selector of OH megamasers for galaxies with high infrared luminosity. In early-type galaxies, which have much lower infrared luminosities, $L_{rm HCN} / L_{rm CO}$ is also a promising tool for discovering OH, but in absorption rather than in maser emission. In addition to dense molecular gas, a radio continuum source and a favorable line-of-sight to the observer are likely key factors in detecting OH absorbers.
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