Does A Hat In Time have co-op?

It appears that no coop exists for the current version of the game until the first content patch. If the Steam page does not say it, it most likely does not have it. See Left 4 Dead 2's Steam page for comparison. It lists Coop as one of its features.

I found a rather brief Steam post dated October 8th 2017 saying it will be released in the next patch.

The Game Wiki states on its Co-op page:

A Hat in Time allows for both local split-screen co-op and online co-op. Local co-op is planned to be implemented in the first major content patch, and internet co-op "later".

As of 13 September 2018, A Hat in Time now includes local split screen co-op. This is included in the base game, and can be accessed from the pause menu - just select co-op, and now a second player can control using a second input. This is what the second player character (Bow Kid) looks like:

Note: The other answers mentioning that Seal the Deal is required are inaccurate - the co-op is released on the same day as the DLC, but is available without it.

Source:

• https://support.hatintime.com/hc/en-us/articles/360008320093-How-does-the-Co-Op-work-
• https://store.steampowered.com/app/924490/A_Hat_in_Time__Coop/