In the case of Picard v. Connor, 1971, the U.S. Supreme Court ruled that before a federal court can hear a state prisoner's petition for habeas corpus (a legal action through which a person can seek relief from unlawful detention), the prisoner must first exhaust all available remedies in state courts or demonstrate that such remedies are either ineffective or unavailable. The petitioner in this case was an inmate who had been convicted of murder and sentenced to life imprisonment by Connecticut courts. He filed his petition directly with Federal District Court without seeking any post-conviction relief at the state level, arguing that he had been denied effective assistance of counsel during his trial because his lawyer failed to object to certain evidence introduced against him by prosecutors. However, since he hadn't pursued these claims within Connecticut’s judicial system prior to filing for federal habeas corpus relief, the Supreme Court held that he hadn’t exhausted all possible avenues for redress as required under existing law.

In the dissenting opinion for Picard v. Connor, Justice Brennan disagreed with the majority's decision to dismiss a habeas corpus petition due to procedural default in state court. He argued that this ruling was inconsistent with previous Supreme Court decisions and federal law which allowed federal courts to hear such petitions if they were not deliberately bypassed by the petitioner. In his view, there was no evidence of deliberate bypass in this case as it seemed that Connor had simply failed to comply with a complex and confusing state procedure rather than intentionally avoiding it. Therefore, he believed that dismissing his petition on these grounds violated his right to have his constitutional claims heard in federal court.