Yes, the Ohio School for the Deaf (formerly the Ohio Institute for the Deaf and Dumb) still exists, although not in the same location as in the 1870s. Instead of being downtown, it is on the north side of town on Morse Road.

The older records that you would be interested in are at the Ohio Historical Society in Columbus. They have the old student admission records (each volume of which contains brief comments about the faculty and staff changes), and the administration records. The administration records would be more likely to have specifics of your relative's work history at the school.

If you haven't already, you might want to consider the possibility that your relative was deaf himself. Many teachers of the deaf in the 1800s were deaf. However, this changed in the late 1800s/early 1900s as attitudes toward sign language changed dramatically. (Rather than being seen as a natural way for the Deaf to communicate, it was looked down upon as being inferior to teaching the Deaf the "proper" way to communicate -- speech. But that's another topic altogether!) Many Deaf teachers lost their jobs in schools for the deaf in this time period because they were unable to speak.

If you are lucky, your relative was Deaf, because since he was a teacher, he likely went to a school for the deaf (whether the Ohio school or another school). The admission records for deaf schools are quite detailed, especially with giving details of other "deaf-mute" relatives.

Hope this helps.

Amy