McKEAGUE, Circuit Judge. Dwayne Greene was booked into the Crawford County Jail on a Monday afternoon after having his bond revoked for attending a plea hearing while intoxicated. Over the next few days, Greene began hallucinating and exhibiting other symptoms of delirium tremens, a life-threatening complication of alcohol withdrawal that we have long recognized is an objectively serious medical need. See Kindl v. City of Berkley, 798 F.3d 391, 401 (6th Cir. 2015). On Friday morning, Greene suffered acute respiratory failure. He died four days later. Crawford County officials did not provide any medical care to Greene prior to his incapacitation. Instead, they sought only a mental health evaluation from the Northern Lakes Community Mental Health Authority and purportedly relied on that evaluation in deciding not to seek medical assistance.

Greene’s estate filed this suit under 42 U.S.C. § 1983, claiming that several jail officials were deliberately indifferent to Greene’s medical need and that Crawford County is liable for maintaining an unconstitutional policy of not providing medical care to inmates suffering from delirium tremens. The estate also brought the same claims against the mental health authority and its employees. The district court denied qualified immunity at summary judgment to some of the county officials and denied summary judgment to Crawford County on the estate’s municipal-liability claim. The county officials and Crawford County bring this interlocutory appeal, and the estate cross-appeals. For the following reasons, we affirm in part, reverse in part, and dismiss for lack of appellate jurisdiction Crawford County’s appeal on the estate’s municipal-liability claim.