Christina Swarns, the litigation director of the NAACP Legal Defense and Educational Fund, who had filed a brief in support of the plaintiffs, called it “a shot across the bow to other metropolitan areas.”

Robert Soard, an assistant county attorney for Harris County, said the county was reviewing the court’s decision and had not decided whether to appeal.

The practice of demanding money as bail is standard in the majority of jurisdictions in the United States. But a series of lawsuits and a growing body of research has led to questions about its efficacy and potential disparities based on race and income. In January, New Jersey dropped its money bail system for minor crimes, and Colorado has changed its bail systems. The discussion has been percolating in other states, as well.

The challenge in Harris County has drawn the support of the new sheriff, Ed Gonzalez, a Democrat, and one of the 16 criminal court judges who are defendants in the case, Darrell Jordan, also a Democrat. The other 15 judges, all Republicans, continue to oppose it, a spokesman said. The county has retained Charles J. Cooper, a high-profile conservative litigator, to help in its defense.

Lawyers for Harris County have pointed out that it has already started making substantial changes to its bail system, including a planned switch to more sophisticated method of setting bail that takes into account how likely an arrestee is to flee or commit a new crime. And they have argued that the county’s policies adhere to Texas’ laws on criminal procedure law, that they do not violate the Constitution and that they are not intended to needlessly detain arrestees.

The order issued on Friday takes effect on May 15. People arrested on misdemeanors charges are to be interviewed about their financial conditions for an affidavit. Those who have been deemed eligible for release at a hearing will have the option of being released within 24 hours of their arrest, regardless of whether they can afford bail.