The Republican-dominated legislature will now have four months to decide whether to legalize the use and cultivation of small amounts of marijuana.
If it fails to act, the Coalition to Regulate Marijuana Like Alcohol can gather nearly 133,000 additional valid signatures to put the measure on the Nov. 8 ballot.
The group wants to allow adults 21 and older to buy and possess 2.5 ounces (71 grams) of marijuana and grow up to six plants per person, 12 plants per household.
Ohio legalized medical marijuana in 2016, with dispensaries opening in early 2019.
Group spokesperson Tom Haren said Friday in a statement, "We are ready and eager to work with Ohio legislators over the next four months to legalize the adult use of marijuana in Ohio,"
Haren added that the group is prepared to collect the signatures needed to put the issue on the ballot.
Two Republican House members in December introduced a recreational marijuana bill, while the Republican Senate last month approved a measure to expand the state's medical marijuana program.