There is no counterpart to this kind of petition in the English-speaking world because courts do not determine facts. On the contrary, facts must be proven to the courts so that the courts can adjudicate the relevant case.

A court, however, can be asked to make a legal, rather than factual, determination, i.e., to declare the rights and duties of the parties under the law. A petition to this effect is called a petition for declaratory relief. The court's decision in such a case is called a declaratory judgment of declaratory ruling.

Since there is no established expression in English for the phrase in this question, it has to be translated from scratch. I would suggest:

petition for determination of fact (or facts)
petition for establishment of fact
petition for factual determination
petition for judicial determination of facts
etc.