Hi all,
Where would you think the Intellectual Property rights for a movie would be?
Would it be the publisher/ movie studio, the producer, the story writer, etc.
I'm thinking about doing a game with reference to a movie.

The rights would be owned by the studio who made it, or possibly by the production company or distributor who got it out to the public or funded the project.

You need to make some phone calls, with an actual phone, to the company. Tell them you are interested in talking about product licensing with movie-branded product. It will almost certainly require multiple phone calls to multiple companies, and getting redirected between licencing agents, marketing agents, legal groups, brand managers, and that is just to figure out who owns the rights.

Note that unless you are planning on working with a tiny indie film nobody has heard of, it will be difficult to get a deal. If you are a large established game studio they may be willing to work with you to get a branded product. Even if you have a big name, know that using their product means you are buying rights to their names and characters, and they will have strict requirements and pay for the privilege of doing so. And even if you are growing and established studio with a great track record, the rights may have already been specified in existing contracts; major film studios have big contracts to license products out to major game studios, often with rights to contract the work out to smaller studios, so you would need to go through a chain of first refusals before acquiring the license.

Building branded products is not easy. The companies have strict lists of what must be done with the product, what must not be done with the product, how elements are to be used and not be used, and more. For movie tie-ins you may be required to use specific actors and pay all their fees and costs. You may be required to only work with certain individuals, such as only using SAG (Screen Actors Guild) members for all voice acting.

Some questions to ask before you start making phone calls: Why would they trust their brands (the movie brand, the studio brand, the star's brands), which may be worth many millions of dollars, to your game? Why would they risk having you produce a bad product, which in turn would reduce their brand value? What have you done to prove that it is worth that risk? What are you offering in exchange for the license, since these deals are usually valued in multiple millions of dollars?

Assuming you want to go forward with the idea, it will likely cost you several hundred thousand dollars for the smallest indie movie names, millions for a movie that has ever shown in major theaters. And get your lawyers involved early, because you will want a legal team to help craft, negotiate, and review all the contracts.

It depends on the movie. It can be with the production company, the studio, an investment consortium, an individual who worked on the movie, a lawyer, a liquidation company. I've even come across movies who's IP has been owned by the church.
The thing is it just isn't easy to find out who owns the IP without doing the leg work of finding out. Also finding out who owns the IP is only the first step. Some IP has heavy restrictions on how and where you can use it so even if you manage to track down the rights holder and gain licensing permission you may have to rethink some of your game plans or even be prepared to add content to your game that is demanded of by the rights holder.