It depends on what went wrong, and often more than one party shares responsibility. If the injury came from poor maintenance, operator error, or unsafe operation, the park is usually responsible — including for how it trained and supervised its staff. A maintenance contractor hired by the park can also be involved.
If the ride or a component was defectively designed or manufactured, its maker can be responsible under product-liability principles, alongside or instead of the park. Establishing this depends on the ride data, maintenance and inspection records, and expert examination of the ride itself.
Because this evidence is controlled by the park and can be lost, acting quickly to preserve it is important. A prompt investigation is how every responsible party — park, contractor, or manufacturer — is identified, which protects your ability to recover.