Do you have an obituary index or newspaper index?
The library maintains a hard copy clipping file of obituaries at the W. Dale Clark branch in downtown Omaha, on the 3rd floor. The records in this file are from 1977 onward. You may also try Omaha Obits, an online index of obituaries extracted from the Omaha World Herald printed before 1977 (many from the early 1900's). It can be found here: http://www.omahaobits.wordpress.com. Please remember that obituaries are basically paid for like advertisements. Not everyone who died had one in the paper.
You may find the information you are looking for using the links on our genealogy page. http://omahalibrary.org/books-and-resources/genealogy
We also provide access to digital archives of the Omaha World Herald and other newspapers on our website's Resource Center: http://omahalibrary.org/resource-center. Select "Newspaper" as the Category.
Other than that you might want to ask our genealogy department for help directly either by filling out their online form (http://omahalibrary.org/component/chronocontact/?chronoformname=genealogy&id=9) or emailing them at firstname.lastname@example.org. It might help them if you have any specific information on the individual for whom you're looking, Please note that there may be a charge for their services, but they will let you know.
Good luck in your search!