Short answer. It depends on the error. A clerical or typographical error, a first-name change, or the day/month of birth or sex entry can now be corrected administratively with the local civil registrar under Republic Act No. 9048 and Republic Act No. 10172; a substantial correction still needs a verified court petition.
What the law says
Any person interested in any act, event, order or decree concerning the civil status of persons which has been recorded in the civil register, may file a verified petition for the cancellation or correction of any entry relating thereto, with the Court of First Instance of the province where the corresponding civil registry is located.
Rule 108, Section 1 — Who may file petition. Read the full provision →
What Rule 108 says on its face
As written, Rule 108 gives any interested person the right to file a verified petition for the cancellation or correction of any entry in the civil register, filed with the court of the province where the corresponding civil registry is located. This is a judicial remedy — a petition filed in court, verified under oath, addressing an act, event, order, or decree concerning a person's civil status that has already been recorded.
Why not every correction goes to court anymore
This text no longer describes the only path available. Republic Act No. 9048 (2001) and Republic Act No. 10172 (2012) opened an administrative route through the local civil registrar for specific, narrower kinds of errors: clerical or typographical mistakes, a change of first name, and the day and month of birth or the sex entry, where the error is clerical in nature. For those categories, a person does not need to file a court petition at all.
When the judicial route under Rule 108 still applies
Substantial corrections — changes that go beyond a clerical or typographical slip, such as corrections affecting a person's actual civil status, nationality, or legitimacy — still require the judicial proceeding this rule describes. For those, a verified petition still needs to be filed in court, in the province where the civil registry entry is recorded, following the process Rule 108 sets out.
Where to file it today
The text names the Court of First Instance as the filing court, which was the trial court of general jurisdiction at the time this rule was written. That court has since been reorganized into what is now the Regional Trial Court. So for a correction that genuinely requires this judicial process — a substantial correction, not a clerical one — the petition goes to the trial court with jurisdiction over the province where the civil registry entry is located, following the province-based venue rule this provision sets.