Themaser pumping schemes proposed for the various OH lines may not be as clear-cut as they once seemed. The main OH lines, at 1665 and 1667 MHz, are thought to be radiatively pumped, with the radiation typically coming from nearby ultracompact HII regions. Recently, a new class of main-line maser has been posited, collisionally pumped by shocks due to molecular outflows. The W3(OH)/W3(OH)-TW system is the archetype: traditional OH masers are excited by theW3(OH) ultracompact HII region, while collisionally pumped OH masers arise in the younger object W3(OH)-TW, which is driving an outflow. The 1720 MHz OH satellite line maser, typically found in SNR-cloud interaction regions, is thought to be collisionally pumped, as are class I methanol masers found in star formation regions. Thus it is plausible that these two masers arise in similar (shocked gas) circumstances. In this study we observe all four OH transitions in the direction of Extended Green Objects (EGOs) that trace shocked gas (possibly from outflows) in high-mass star formation regions. Previous studies have found a high incidence of class I methanol maser emission in these objects, suggesting that OH(1720) masers might also be abundant in this sample. Observations of 20 northern EGOs (δ > -17°) were carried out with the Jansky Very Large Array of all four ground state OH transitions, the HI line, and the 20 centimeter continuum. Positive detection of OH lines was obtained for 10 EGOs: OH lines at 1665 and 1667 MHz were detected toward 45% of the sample. The stellar OH line at 1612 MHz was detected toward 15% of the sample. The 1720 MHz emission line was detected in only one EGO source, G45.47+0.07, which is also presents the strongest main-line OH emission of our sample. We measure the projected separations between OH masers and GLIMPSE point sources associated with EGOs (median value 0.04 pc), betweenOH and class II methanol masers (median value 0.03 pc), and between OH and class I methanol masers (median value 0.14 pc), thus confirming previous findings that class I methanol masers are located further from exciting sources than areOH and class II methanol masers. Bearing in mind the theoretical incompatibility of class I and class II methanol maser pumping schemes, and the obtained separations between class I methanol masers and other masers in the EGOs, we conclude that class I methanol masers do not co-exist with GLIMPSE point sources, OH and class II methanol masers in one and the same core. Rather, we suggest that the class I masers arise in distinct but neighboring cores, about 1 pc distant, and in a different evolutionary state.