*521In an action, inter alia, to recover damages for false arrest and deprivation of civil rights pursuant to 42 USC § 1983, the plaintiff appeals from so much of an order of the Supreme Court, Kings County (Partnow, J.), entered March 9, 2004, as granted that branch of the defendants’ cross motion which was to dismiss his cause of action to recover damages for false arrest, and denied stated portions of his motion to compel discovery.
Ordered that the order is modified, on the law, by (1) deleting the provision thereof granting that branch of the cross motion which was to dismiss the cause of action to recover damages for false arrest and substituting therefor a provision denying that branch of the cross motion, (2) deleting the provision thereof denying that branch of the motion which was to compel discovery of document request 12 seeking “[a] 11 records of injuries sustained by detainees in the holding cells at Brooklyn Central Booking from June 3, 1996, to June 3, 1999,” and substituting therefor a provision granting that branch of the motion, and (3) deleting the provision thereof denying that branch of the motion which was to compel discovery of that part of document request 13 seeking “[a] 11 documents reflecting written or oral complaints from or on behalf of persons who have been detained at Brooklyn Central Booking regarding safety and other conditions at Brooklyn Central Booking from June 3, 1996, through June 3, 1999,” and substituting therefor a provision granting that branch of the motion to the extent of compelling discovery of all documents reflecting written or oral complaints from or on behalf of persons who have been detained at Brooklyn Central Booking regarding safety at Brooklyn Central Booking from June 3, 1996, through June 3, 1999; as so modified, the order is affirmed insofar as appealed from, with costs to the plaintiff.
A showing of probable cause constitutes a complete defense to a claim of false arrest (see Wasilewicz v Village of Monroe Police Dept., 3 AD3d 561, 562 [2004]; Carlton v Nassau County Police Dept., 306 AD2d 365, 366 [2003]). However, probable cause is a question of law, to be decided by the court only where there is no real dispute as to the facts or the proper inferences to be drawn therefrom (see Wyllie v District Attorney of County of Kings, 2 AD3d 714, 718 [2003]; Orminski v Village of Lake Placid, 268 AD2d 780, 781 [2000]). In the instant action, the defendants failed to establish, as a matter of law, that the defendant police officer had probable cause to arrest the plaintiff. Contrary to the defendants’ contentions, there is an issue of *522fact as to whether the officer’s reliance on the statement of the plaintiffs ex-wife was justified where the evidence and testimony indicated that a reasonable person would have made further inquiry (see Carlton v Nassau County Police Dept., supra; Stile v City of New York, 172 AD2d 743 [1991]; Canteen v City of White Plains, 165 AD2d 856, 857 [1990]). Accordingly, the Supreme Court erred in granting that branch of the defendants’ cross motion which was to dismiss the plaintiffs cause of action to recover damages for false arrest.
The Supreme Court also erred in denying that branch of the plaintiffs motion which was to compel discovery of document request 12 seeking “all records of injuries sustained by detainees in the holding cells at Brooklyn Central Booking from June 3, 1996, to June 3, 1999,” and that part of document request 13 seeking “all documents reflecting written or oral complaints from or on behalf of persons who have been detained at Brooklyn Central Booking regarding safety at Brooklyn Central Booking from June 3, 1996, through June 3, 1999.” The plaintiffs cause of action pursuant to 42 USC § 1983 required proof that the defendants City of New York and New York City Police Department were deliberately indifferent to an unjustifiably substantial risk of serious harm of which they were aware, or that the risk was so obvious that it should have been known to them, and that they acted or failed to take reasonable measures despite such knowledge (see Farmer v Brennan, 511 US 825, 847 [1994]; cf. Vargas v 1387 Grand Concourse Realty Corp., 288 AD2d 24 [2001]). The defendants’ failure to challenge the plaintiff’s notice of discovery within the time prescribed foreclosed inquiry into the propriety of the information sought except with regard to requests that are privileged under CPLR 3101, or as to requests which are palpably improper (see Garcia v Jomber Realty, 264 AD2d 809, 810 [1999]; cf. Garner v Garner, 160 AD2d 833, 835 [1990]). In light of the fact that request 12 and request 13, as limited, were both relevant and sufficiently specific to apprise the defendants of the category of documents to be produced, the Supreme Court erred in denying those branches of the plaintiffs motion which were to compel disclosure of such documents (see Stevens v Metropolitan Suburban Bus Auth., 117 AD2d 733, 734 [1986]). Adams, J.P., Santucci, Goldstein and Crane, JJ., concur.