Short answer. It means the court where you filed your Rule 24 petition. Section 5 provides that for purposes of applying Rule 23 to pre-action depositions, every reference to 'the court in which the action is pending' is deemed to refer instead to the court where the perpetuation petition was filed.
What the law says
For the purpose of applying Rule 23 to depositions for perpetuating testimony, each reference therein to the court in which the action is pending shall be deemed to refer to the court in which the petition for such deposition was filed.
Rule 24, Section 5 — Reference to court. Read the full provision →
Why a special reading rule is needed
Rule 23 was originally written for depositions taken during an already-pending, ongoing case, so its repeated references to 'the court in which the action is pending' don't literally fit a Rule 24 petition, where there is no lawsuit pending yet. Without some adjustment, applying Rule 23's mechanisms to a pre-action deposition would leave those references pointing at nothing, since by definition there is no pending action for a petitioner in this situation to point to, leaving the reader stuck without any workable forum for enforcing or resisting the deposition until Section 5 supplies the necessary fix. Rule 24 petitions exist precisely because a prospective party may need to preserve testimony before a suit can even be filed, so without Section 5's fix, that entire pre-action mechanism would be missing the forum needed to actually make it work.
The fix this section provides
Section 5 substitutes the petition court for the pending-action court wherever Rule 23 would otherwise apply, giving protective orders, motions to compel, and other similar Rule 23 mechanisms a clear and workable forum even before any actual lawsuit exists. This substitution is mechanical and complete: everywhere Rule 23 says 'the court in which the action is pending,' Section 5 tells the reader to substitute 'the court in which the petition was filed' instead, so the entire existing machinery of Rule 23 can operate cleanly on a pre-action petition without any further rewriting or careful reinterpretation being necessary. This drafting technique — deeming one phrase to mean another for a defined purpose — lets Rule 24 borrow Rule 23's existing deposition procedure wholesale, rather than duplicating that entire procedural apparatus inside Rule 24 itself.
The practical effect
Parties dealing with disputes over a pre-action deposition simply file their Rule 23-style motions in that same court that granted the Rule 24 petition, rather than in whatever court a future lawsuit might eventually happen to land in. This keeps the petitioning court fully in charge of everything connected to the deposition it originally authorized, from start to finish, instead of splitting authority across two different courts before the underlying civil case has even actually been filed anywhere. It also gives both the petitioner and any expected adverse party a predictable, identifiable forum to raise objections or seek protective orders while the perpetuation proceeding is still ongoing.