Ohio state law doesn't restrict "dating," in the sense that two people might go out to dinner and a movie together. However, Ohio law does set the age of consent in the state at 16 years old. Generally, if an adult engages in sexual conduct with a minor under the age of 16, that adult has committed statutory rape.
TL;DR (Too Long; Didn't Read)
The legal age of consent in Ohio is 16. Minors under the age of 16 cannot engage in sexual conduct with an adult over the age of 18.
Minors 15 and Under
A minor under the age of 16 cannot engage in sexual conduct with an adult over the age of 18. The penalties are most severe for sexual conduct with a 13- or 14-year-old minor. An adult over the age of 18 who engages in sexual conduct with a 13- or 14-year-old is guilty of a felony.
Under Ohio law, minors between the ages of 13 and 15 are legally allowed to engage in sexual conduct with another minor between the ages of 13 and 17.
There is a knowledge component to Ohio's law. However, pleading ignorance generally is not an excuse. A judge can find an adult guilty of statutory rape if she was "reckless" in assuming the minor's age. For example, if an 18-year-old claimed he didn't know how old his girlfriend was, but knew she was in seventh grade, the judge would probably consider that reckless.
Minors 16 and 17 Years Old
The age of consent in Ohio is 16, so 16- and 17-year-olds can legally engage in sexual conduct with an adult. However, an adult can still be convicted of statutory rape of a 16- or 17-year-old if he is in a position of power over the minor. Sexual conduct between a student and a teacher, or a student-athlete and a coach, would fall into this category.
Even if the relationship doesn't constitute an age-related offense, the adult could still be brought up on charges of contributing to the delinquency of a minor or interference with custody. The latter charge would come into play if, for example, the minor ran away from home to live with an adult significant other.
Proximity of Age
Generally, illegal sexual conduct with a minor is a fourth-degree felony in Ohio. However, the difference in age plays a role in the severity of the sentence if an adult is accused of violating Ohio's age of consent law. For example, an 18-year-old high school senior might be dating a 15-year-old high school sophomore. While sexual conduct would still violate Ohio's age of consent law, it would only be considered a misdemeanor offense.
If the adult is 10 or more years older than the minor, illegal sexual conduct is a third-degree felony. However, if the adult is less than four years older than the minor, illegal sexual conduct is a first-degree misdemeanor.
If a minor is legally emancipated, she has all the rights and privileges of an adult despite her age. However, unlike many other states, Ohio does not have a specific law dealing with emancipation of minors. Rather, a judge would consider the minor's circumstances in determining whether to consider her legally emancipated.
If the minor is married, enlisted in the armed forces, or self-supporting and living on his own, he is more likely to be considered emancipated. The age of consent law would not apply to a minor who was considered emancipated. However, as a practical matter, most emancipated minors will be over the age of 16 anyway.