Maybe what you saw was a wild animal? A deer or a raccoon or a monkey(,) perhaps?
Do I need the comma before perhaps?
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I think if perhaps is used as a sentence modifier, and at the end of the sentence, I see comma there.
Collins Dictionary quotes it with an example:
"he'll arrive tomorrow, perhaps" -with a comma.
But then, if you are not sure about the options separated by 'or', I see there's no comma.
Cambridge Dictionary has an entry almost close to your example:
"We plan to travel to Europe - to Spain or Italy perhaps." -with no comma.
Several resources, such as the Purdue Online Writing Lab's article, Commas with Nonessential Elements, indicates that non-essential words or phrases in a sentence should be separated with a comma.
In your example, it seems that the essential part of the second sentence is the list of possible animals, as they are mentioned in contrast to the alternative that the thing seen wasn't a wild animal. "Perhaps" is kind of implied since the speaker also didn't witness whatever the other person saw, therefore it's non-essential and I'd put a comma in front of it.
Unless there is some reason why you prefer not to, you could phrase it this way:
Maybe what you saw was a wild animal? A deer, a raccoon, or perhaps a monkey?
Otherwise: Maybe what you saw was a wild animal? A deer, a raccoon, or a monkey, perhaps?
In the second example, I would set it off with a comma for reasons stated by others, but also simply because it sounds natural to pause after "a monkey," as if perhaps was an afterthought.