Joseph H. Crane was born in Elizabethtown, New Jersey, the son of William and Abigail (Miller) Crane. William Crane was with Richard Montgomery in the Battle of Quebec and in the service of General George Washington, lost a leg in the Battle of Brandywine, at the head of his regiment. He was a major of an Essex County, New Jersey regiment in the Revolutionary War and made a general of the militia after the war. William was a son of Stephen Crane, a notable citizen of Elizabethtown and a delegate from New Jersey to the First Continental Congress in 1774.

Joseph Crane was a student at Princeton College. He studied law with Governor Aaron Ogden and was admitted to the bar of New Jersey in 1802 and practiced there briefly. He came to Dayton, Ohio in 1804 and immediately became legal counselor to Daniel C. Cooper. He was the first attorney to practice in Dayton, although at that time there was little need for a lawyer in general practice. However, in those early years when Ohio was newly admitted to the Union and was being organized, Dayton municipal institutions were being formed, and methods of procedure established - men of legal learning, instructed in the principles of the new representative system of Federal and State government and in the history of English constitutional liberty, were in high demand.

In 1809, Joseph Halsey Crane married Julia Ann Elliott, the daughter of one of Dayton’s first doctors, Dr. John Elliott, who was a surgeon in the United States Army during the Revolution and had been at Vincennes, Indiana with General "Mad Anthony" Wayne and General Arthur St. Clair. Joseph and Julia had a large family, but most of the children, like Ann (died February 22, 1812, aged 18 months), died young. Two sons, William Elliott Crane and Joseph Graham Crane, followed their father into the legal profession.

Joseph Crane served in the War of 1812 as a private, Fifth Brigade, First Division of the Ohio Militia. He was elected a member of the Ohio House of Representatives in 1809. During the session in Columbus, Ohio, he authored the Practice Act - modeled after the practice of the Court of Common Pleas at Westminster Hall - under which legal proceedings in Ohio were regulated until the adoption of the revised constitution of 1851.

He was Montgomery County recorder in 1813 and prosecuting attorney of the county from 1813 to 1816. In 1814, he was on the Board of Directors of Dayton’s first bank, the Dayton Manufacturing Company. In 1819, he was a Trustee at the founding of the Dayton Academy.

Joseph Halsey Crane was elected President Judge of the Ohio First Circuit Court of Common Pleas in 1817 serving two terms until he resigned in 1829 to take his seat in Congress. He was elected in 1828 as an Anti-Jacksonian from Ohio's 3rd congressional district to the Twenty-first Congress. He was subsequently elected to three more terms, serving until 1837. He declined to be a candidate for renomination in 1836.

Joseph H. Crane returned to Dayton after his congressional service and resumed the practice of law. For several years from 1831, he was in partnership with Robert C. Schenck. When Clement Vallandigham came to Dayton in 1847 and became actively engaged in the practice of law a few years later, he often availed himself of the superior facilities afforded by Judge Crane's extensive law library in preparation of his cases. Judge Crane mentored and encouraged the aspiring young attorney and a warm personal friendship developed between them that was never broken.

Joseph Halsey Crane died in Dayton and was interred in Woodland Cemetery, Dayton, Ohio.