"Red tape" refers to the rules that governmental personnel must follow to accomplish a task. Sometimes the governmental process seems cumbersome to us, especially when we want a quick answer. Many feel that the federal government establishes far too many rules or procedures with their numerous governmental departments---even more so than state governments, which are closer to and more quickly responsive to its citizens. So, you can see how "red tape" has a direct connection to any governmental level and especially the federal government.
This term began in the late 17th century. I've included a web site, so you can explore its beginnings a bit more.