This is far too open question to have a single answer, and you should probably put the question in the right context for us to help.
For instance, any of the developers could come up with an entire database model to fulfil theirs specific needs for their platform, so you could have a local specific Android database, a local iOS database, a local front-end database or database-like storage models and then we have the backend guys.
For now, I'm assuming you're talking about an application which is fully served by some arcane business logic that resides in the backend and from which all other platforms will leverage by the use of some kind of services/REST architecture (it's a big leap of assumptions I'm taking here).
If this is the case, everyone product-related (that excludes CEO and CFO, for example) should be together discussing what the system should do, and everything discussed should impact the database at some point somehow. That being said, the database design should be left to the technical guys which will develop the application, with the final word from the most senior developers for that product (people who knows well the impacts of a new single field or the removal of an old field, for example).
That's why you have senior developers (you do have them in your team, right ?) You pay a lot to hire smart guys, let the smart guys do their job. (Joel Spolsky has a nice article not exacly about this but with some nice insights).
This quote in particular is interesting:
There were some great examples of this. Managers always refused to resolve conflicts. Typically what would happen is that a designer would get into an argument with a developer over what a feature should look like. They would argue back and forth, discussing the issue for an hour, and eventually, failing to reach agreement, they would stomp into some manager’s office hoping for a resolution. Now you’ve got three people in the room: a designer, a developer, and a manager. Who’s the person who knows least about the problem? Obviously, it’s the manager — who was just hauled in at the last minute for Conflict Resolution. At Microsoft, the manager would usually refuse to make the decision. After all, they have the least information about the problem. The manager would generally force the designer and developer to work it out on their own, which, eventually, they did.