Immediately after crossing the Big Blue River, IN-252 turns left and heads east. To follow the Madison State Road, you need to continue on Eisenhower Drive as it approaches Edinburgh. The road did not go through the main street of Edinburgh. It passed two blocks to the west.
Amusingly, the Town of Edinburgh's web site has a Frequently Asked Questions section with three questions, the last of which is "What county and township is Edinburgh in?" The answer is "Edinburgh is in three counties - Johnson County/Blue River Township, Bartholomew County/German Township and Shelby County/Jackson Township." Now that is confusing!