I often see online requests for someone to help with an obituary in older versions of the Middletown Press or the Penny Press, its precursor. The request is actually more complicated than most people think. Except for recent years, the Press has not been digitized. It is only available on microfilm.
For most researchers, that would make the Connecticut State Library their first stop. The CSL microfilmed many local newspapers as part of a preservation project in the 1990s. While the CSL is a good resource, it would not provide you with a complete picture. The CSL only has records from 1919.
In this case, Russell Library has the most complete collection available. Microfilms cover most of the paper's run. And, if you do not have an exact date, they have an index to the papers from the early 1900s. Contact them at www.russelllibrary.org. Librarians will do their best to help with your research.