Yes. We have birth records for the City of Cincinnati covering 1874-1909 and death records for the City of Cincinnati covering 1865-1909. These records have been digitized and are now available online.
Births and deaths inside the City of Cincinnati corporation limit after 1909 may be obtained by contacting the Cincinnati Health Department:
Vital Statistics Office
1525 Elm Street, 4th Floor, West
Cincinnati, OH 45202
Phone: (513) 352-3120
Births and deaths before 1909 in Hamilton County, Ohio but outside the City of Cincinnati may be obtained through the Hamilton County Probate Court. These records have been digitized and are freely available online at http://www.probatect.org/courtrecordsarchive/bukcats.aspx.
Brths and deaths after 1909 in Hamilton County may be obtained by contacting the Ohio Department of Health:
Ohio Deptartment of Health, Vital Statistics
35 E. Chestnut St.
P.O. Box 15098
Columbus, Ohio 43215-0098
Phone: (614) 466-2531