Anyone hiking Katahdin is supposed to have a day use permit (even if you don't have a car). You must exit the park the same date of the permit. To day hike in to the park, and back out...is not something most people choose to do. Katahdin is not just a quick scamper for most people.
Here is the link to the Baxter State Park Reservations page:
http://www.baxterstateparkauthority.com/reservation/
For more information on the AT within Baxter, please look under the "Hiking" header, then "Hiking Info" sub-header.