I was dreading someone asking that…I won’t say, as there are too many earnest members waiting to be triggered, no matter how I answer!
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No, we don’t! 
…We use garage! We use parkade for large commercial parking garages.
They use car park at Toronto airport I think and in the UK but I have never heard it with any regularity.
Is the guy possibly saying that he needs a guide? or that he wants to stay in a specific room or suite he saw in some guide? Fun mystery!
I’m Canadian and live on the West Coast and never hear Car Park even when talking about the multi-level car “garages”. 
Parkade is the norm.
I only hear Car Park when speaking to English/UK people…
How is it pronounced? Park-aid or as in French Park-add?
park -aid as in kool-aid
I’m in Toronto have never heard car park except when talking to folks from the UK. Parkade is an older term here, so not very common, either.