No extra fee, Just the 20 to park
You can self park at all the resorts at no additional fee if you are staying there. The delux resorts have valet parking for an additional fee per day. There's no additional fee for handicap parking. At the parks there is a parking fee unless you are an annual pass holder.
If you're staying at any of the Disney properties there is no charge or fees for parking. They do have handicap parking regardless of where you are staying but again you may be subject to a parking fee depending on where you are staying!
There is no extra fee, you pay the standard $20 but you need to show a valid disability Parking Permit.
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