Complimentary- something given or supplied without charge, as lodging, transportation, or meals, esp. as an inducement to prospective customers.
Complementary- forming a complement; completing.
My guess is that “Complementary Parking” means the parking is in addition to some other service (apartments and hotels have “complementary parking”) and “Complimentary Parking” is like free valet or free parking garage.
Complimentary is the word that should be used here. That means “with compliments” or “on the house.” Complementary does not make sense in this situation, as it refers to two or more things which fit together or are compatible.
free parking/the spelling of the word
Means you don’t have to pay for parking.
Someone used spell check without using his/her brain!
Where’s letter man when you need him?