To make sure the records you're looking for are likely to be held by the State Archives, please visit the Search Archives Holdings page at https://www.in.gov/iara/services-for-public/search-archives-holdings/ .
Then you can contact the Archives by calling (317) 591-5222, emailing arc@iara.in.gov, or sending postal mail to: Indiana State Archives | 6440 E. 30th St. | Indianapolis, IN 46219.
For mailed requests, both postal and electronic: Give a short but detailed explanation of the records you are seeking, including any relevant names and dates. If you have already located the specific records you need in the Research Indiana catalog, it's also helpful to include the Page ID, Local ID and Level ID from your catalog search results page. Finally, provide a phone number or email address at which you prefer to be contacted for clarification of your questions and any copying fees that may result, and a clearly written or typed postal address to which any paper records may be mailed.
If emailing, also be sure to use a clear, specific subject line: Civil War, Soldier's Home, Hospital Records, Morton Telegrams, etc.