Coleman is talking about cases in which no indictment is filed, which is different than no charges being filed. He consistently conflated those 2 concepts during his argument and briefing. Ds may be arrested and released without charges w/in 48 hours of arrest, but once they are brought before a magistrate they are accused of a crime, usually via a preliminary charging document such as a complaint.That clears things up somewhat, but even defining "charges" as "indictments" (an "information," for misdemeanors), which does indeed conflate the two terms, I can't find any data supporting Coleman's assertion that such cases represent half of arrests. The closest on-point estimate I'm aware of came from a 2005 study (pdf) performed by the Public Policy Research Institute at Texas A&M on behalf of the Texas Indigent Defense Task Force (see pp. 28-29):
Since implementation of the FDA’s prompt appointment standard [for jail cases], there exists a widespread perception that counties incur significant costs for attorney’s fees in cases where no charges are filed. Objective data reported by Texas counties in their annual Expenditure Report demonstrates that this concern is greatly exaggerated. In FY 2004, 55% of Texas counties (140 of 254) had zero cases in which an attorney was appointed in a case where the defendant was never charged by information or indictment. At a statewide level, “un-filed” cases represented 2% of all cases in which attorneys were appointed to indigent defendants
So where does this figure come from that as many as half of arrests never result in an information or indictment? No source I can find confirms that, but I'll keep looking.