It seems perquisitio is a Latin term that might be associated with a Search Warrant. At least that is the term that this encyclopedia of Roman Law associates to the expression "search for stolen things".
Notice the Italian for Search Warrant is Perquisizione, derived from the related Latin term (similar in French). Meanwhile, the OED gives the English term "perquisition" (also from the Latin) the meaning of a formal search too:
A thorough or diligent search, especially one made officially; careful investigation or inquiry; (Law) a search of property to find a person, incriminating documents, etc.
More succinctly, Merriam-Webster dictionary defines the term as:
a thorough search
specifically: a search by warrant
There is however another option, also suggested by the encyclopedia of Roman Law linked above, which is quaestio lance et licio, or (simplified, I imagine, from common usage) just lance et licio. The encyclopedia defines this as:
Meanwhile, Brill's New Pauly (subscription-walled) defines this expression as:
(literally 'search with dish and girdle'). In Roman law, this referred to a formal house search (described in Fest. 104; Gai. Inst. 3,192,193; Gell. NA 11,18,9; 16,10,8), conveying to a thief the status of a fur manifestus (a 'manifest thief' or a thief 'caught in the act'); even as early as the 2nd cent. BC, it had already fallen out of common use. The ritual in which the searcher had to appear naked, equipped with lanx and licium, had already become incomprehensible to ancient commentators (Gai. loc. cit. 'res tota ridicula', 'a totally ridiculous affair'). Despite various attempted interpretations (tools to carry any stolen goods that may have been found; magical or sacred relics of an ancient sacrificial ritual, and most recently [1. 177]: measures of capacity and length in order to record and assess the stolen goods), it will probably no longer be possible to identify its original purpose.
Not sure if relevant or not, but here is an academic article in German entitled Lance et licio, published in the journal Usus Antiquus Juris Romani (so might be pertinent). It requires subscription though.
So, in conclusion, perquisitio might be enough for a general term. Lance et licio is clearly an idiom which literally makes no sense in your context, and yet seems to be an established Latin idiom for exactly what you want.