Various spellings of this name occur, including Crashaw, Croshaw, Crosher, Crenshaw, Crozier, and Crosier. It is believed that at least some of them are part of the same family. See more discussion of spelling variations and possible connections in the section about Capt. Thomas Graves.
There is a Crowshaw-Crosher Y-DNA Project at Family Tree DNA to explore the ancestry and relationships of all the various families with some variation of this name. As a start, a Y-DNA haplogroup chart has been created and may be found here. For those in the project who have done Y-DNA testing, it can be seen that there are 3 distinct families. However, it is very possible that we will discover many other results as the project grows. More members of this project are needed.
CONNECTION WITH CAPT. THOMAS GRAVES OF VA (Genealogy 169)
Capt. Thomas Graves of VA was the first European settler in America with the Graves surname. He arrived in Jamestown, VA, in Oct. 1608 from England, as part of the second supply after the original settling in May 1607. Raleigh Croshaw also arrived as part of the second supply. The records do not show the surname of Katherine, wife of Thomas Graves, although most people believe it was Croshaw.
The 4th Edition of the Adventurers of Purse and Person, Virginia, 1607-1624/5, compiled and edited by John Frederick Dorman, states on p. 768 of Vol. 1: "Capt. Raleigh Croshaw, Gent., came to Jamestown in the Second Supply, the latter part of Sept. 1608. He was probably a member of the family of Crashaw of Crashaw, Lancashire, in which the name Richard was common and which had branches at Bentley and Dodsworth in Yorkshire. If such be the case, he was a relative of the Rev. William Crashaw, B.D. (1572-1626), who was born near Sheffield, Yorkshire, and whose eloquent sermon on the colonization of Virginia has been so often quoted, and of the latter's son Richard Crashaw (1613-1649), the Roman Catholic priest and mystic poet."
It has been noted that no place named Crashaw or Crawshaw can be found in Lancashire. Although the statement above in Adventurers of Purse and Person may be wrong, it is also possible that Crashaw Booth (or Crawshawbooth) near Rossendale and Haslingden in Lancashire is the place mentioned. An article in "British History Online" (available by clicking here) states that in 1323 the township of Higher Booths consisted of Croweshagh and four others. The composite township, taken out of the forest, includes Crawshaw Booth, 1,614 acres. It became the custom after the 1300s to lease the vaccaries or booths, and in the latter half of the 15th century the rent for Crawshaw was 6 pounds. (A vaccary is a cow house, a pasture, or other place where cows are kept. The word is usually linked to grazing land in the moors and valleys of the Pennines in Yorkshire and Lancashire, England; a grazing unit of 30 beasts.) However, it should be noted that no Crawshaw was in the list of lessees in the 15th century.
More information about Capt. Thomas Graves and the relationship with the Croshaw family is in the research section of the GFA website in the discussion about Capt. Thomas Graves. Of special pertinence is the paragraph about William Crashawe and his possible connection to Capt. Thomas Graves.
Variations of the name in England and America include Crowshaw, Crashaw, Crawshaw, Crosher, Cranshaw, Crenshaw, Crosher, Crosier, Crozier, and possibly Croser and Crosser. A couple of articles in the Graves Family Bulletin discussed the ancestry and some of the changes in the name in America. Those articles can be seen here. There are also surname forums on Genealogy.com for variations Crawshaw, Cranshaw, Croshaw, and Crenshaw.
One source for learning about family and its distribution in England and America is on Ancestry. Entering the spelling variants of the name will give the meaning and history of the name, where the family lived in the U.S. and the U.K., and other information.
It is believed that if sufficient autosomal DNA tests were run on known descendants of Capt. Thomas Graves of genealogy 169 and known descendants of Croshaw ancestors, we might be able to confirm whether or not Katherine was indeed a Croshaw. If we could find direct all female ancestral lines back to Katherine and a known female Croshaw, we might also be able to use mitochondrial DNA testing to verify ancestry.