Hernando County School District's schools has a pop out Let's Talk contact feature that further utilizes a drop down menu to make a user's request specified. For example, clicking on the "Brooksville Elementary" tab allows for elementary related questions, whereas many of the other tabs are district wide topics. Check out their website to see how this helpful feature works.
Landing Pages for Operations
Dallas ISD's Let's Talk! page has a list broken down my department where users can submit questions or concerns. The lists are extensive and cover numerous areas in a school district's operation. Check out their page here.