There is a somewhat hidden resource for Hamilton County, Indiana researchers that the Health Department has placed online. You can now search for death records of your Hamilton County ancestors and relatives.
The site is located here, somewhat hidden by the fact that the link is located not at Vital Records, but tucked away under Online Food Inspection Reports! Click on the Vital Records link from this page, and begin searching away.
According to their website, "The Hamilton County Health Department maintains electronic vital records from approximately 19xx to 2006. The Health Department database does not include all Hamilton County Death Records."