WASHINGTON — A unanimous Supreme Court signaled yesterday that some courts are going too far in barring lawsuits by inmates complaining about their treatment.

In an opinion by Chief Justice Roberts, the court overturned procedural obstacles in the 6th U.S. Circuit Court of Appeals that led to dismissal of civil-rights complaints brought by three Michigan inmates.

The appeals court in Cincinnati covers the states of Michigan, Ohio, Tennessee, and Kentucky. Federal courts in the circuit allowed just 18 of nearly 500 inmate civil rights suits to proceed, a recent American Civil Liberties Union study concluded, making the circuit the most restrictive in the country for such lawsuits.

The Republican-controlled Congress passed the Prison Litigation Reform Act in 1995, seeking to slow a flood of federal lawsuits.

The law requires prisoners to go through a lengthy administrative grievance process before they may sue in court.

The law worked — too well, according to critics. Nearly 42,000 civil rights petitions were filed in 1995 before the law took effect. Five years later, the number was down to 26,000, according to the Justice Department.

“Today’s decision will at least help to ensure that the courthouse door is not completely shut,” ACLU legal director Steven Shapiro said in a statement.

Justice Roberts wrote that under the prison reform act, inmates are not required to demonstrate that they have exhausted the administrative complaint procedure. The chief justice said a lawsuit is not necessarily invalid just because a defendant was not named in the inmate’s earlier administrative grievance. In addition, Justice Roberts wrote, the prison litigation law does not require dismissing the entire lawsuit when an inmate fails to exhaust some of his claims administratively.

The Supreme Court is “not insensitive to the challenges faced by the lower federal courts in managing their dockets and attempting to separate … needles from haystacks,” Justice Roberts wrote.