Short answer. At least twenty calendar days. Section 3 requires the petitioner to serve the named prospective adverse parties with the petition and a notice of the hearing, and the court must cause notice of that hearing to be served on the parties and prospective deponents at least twenty calendar days before the hearing date, in the manner used for summons.
What the law says
At least twenty calendar days before the date of the hearing, the court shall cause notice thereof to be served on the parties and prospective deponents in the manner provided for service of summons.
Rule 24, Section 3 — Notice and service. Read the full provision →
Two layers of notice
The petitioner personally serves a notice, together with a copy of the petition, on each expected adverse party named, stating that the petitioner will apply to the court at the specified time and place for the order described in the petition. Separately, the court itself must cause notice of the hearing to be served on the parties and prospective deponents, using the same manner used for summons. Both layers bind the petitioner in different ways: one is a service the petitioner personally carries out, and the other is a service the court itself must cause to happen before the hearing can proceed.
The twenty-day minimum
That court-issued notice must go out at least twenty calendar days before the hearing date — protecting people who have not even been formally sued yet from being drawn into a testimony-perpetuation hearing without adequate warning. Twenty calendar days means the full period is counted in ordinary days, not just business days, and the section fixes this as a floor rather than a ceiling — the court can allow more time before the hearing, but the notice cannot go out any later than twenty days beforehand without falling short of what Section 3 requires.
Why summons-style service is required
Because these are prospective parties who have no case pending against them yet and likely have no counsel of record, the section borrows the more rigorous service-of-summons standard rather than the lighter service typically used for ordinary motions. Summons-style service is generally more exacting than ordinary notice because it is designed for situations where a person is being brought into a legal proceeding for the first time, with no prior appearance or counsel of record to rely on for effective delivery. Using that same standard here reflects the fact that a prospective adverse party in a perpetuation-of-testimony petition is, functionally, in exactly that position — someone with no existing foothold in litigation who still needs to be reliably reached.