1Ives Family, The Connecticut Nutmegger, Vol. 32, p. 200 (Sep. 1999).
This source mentions a different William Bassett (1621-1684) of New Haven who married Hannah Dickerman (1621-1665) in 1648 while the William Bassett (1624-1670) of Massachusetts was still married to Mary Raynesford (1632-1694).
"WILLIAM IVES was born in England about 1605, and died in New Haven, CT about 1648. He married in New Haven, 4 June 1639, HANNAH DICKERMAN (New Haven VRs), who was born about 1621. She is thought to be the daughter of Thomas Dickerman and Eleanor Whitington. William arrived in Boston November, 1635 on the Truelove (Coldham, Complete Book of Emigrants) and moved to Quinnipiac (now New Haven) about 1638, where he was one of the original settlers. His will was made in New Haven 3 April 1648; it shows that he had two sons, John and Joseph, and at least 2 daughters, Phoebe and Martha, all minors at the time of his death; his wife was named executor, responsible for the bringing up of the children. His widow Hannah married a second time William Bassett about six months after the death of William Ives, 7 November 1648 in New Haven."2Ernest W. Elliott, Which William Bassett is of New Haven?, The Connecticut Nutmegger, Vol. 40, p. 149 (Jun. 2007).
This shows that the other William Bassett (of New Haven) marrying Hannah Dickerman did not marry anyone other than Hannah Dickerman.
"William Bassett took the oath of fidelity in 1644. At about age 27, he married Hannah Dickerman, widow of colonist William Ives, 7 November 1648 in New Haven. This was Williams first and only marriage. He was a member of the Colony train band (militia). He and Hannah had four children - Hannah, John, Samuel, and Abiah. John and Samuel passed beyond New Haven first into Hamden, CT and then into North Haven, CT. William's wife Hannah died 6 November 1665 in New Haven at about age 44. William died 18 years later on 29 August in New Haven. His name appears a number of times in Colony records."
1James A. Rasmussen, Edward Raynesford of Boston: English Ancestry and American Descendants, NEHGR, Vol. 139, p. 296-299 (Oct 1985).
"7. EDWARD RAYNSFORD was baptized at Staverton, co. Northampton, England, 10 Sept. 1609 (Isham Longden MSS Northants Register 11, "St. John the Baptist, Staverton" 14, Raynsford pedigree in Miscellanea Genealogica et Heraldica, 3rd series, 2 [1896-97];159), and died at Boston, Mass., 16 Aug. 1680 ("Hobart Journal." Register 121 [1967]:206).
. . .
The name of his first wife is unknown, but she died at Boston, 4 mo. 1632 (Report of the Record Commissioners containing Boston Births, Baptisms, Marriages, and Deaths, 1630-1699 [Boston, 1883], 1:1, hereafter Boston VRs). He married second before 15 10 mo. 1633 (when she was admitted to the First Church as his wife) ELIZABETH ----- (Records of the First Church, 1630-1868, Publications of the Colonial Society of Massachusetts [Boston, 1961], 39:17), who died at Boston, "Mrs. Rainsford, the aged Mother, " 16 Nov. 1688 (Samuel Sewall, the Diary of Samuel Sewall, 1674-1729, ed. M. Halsey Thomas [New York, 1973], 1:176).
. . .
Children by first marriage, recorded at Boston:
i. JOSHUA2 (or Josiah), twin, b. 1 4 mo. 1632, bp. 17 4 mo. 1632; d. 7 mo. 1632.
ii. MARY, twin, b. 1 4 mo. 1632, bp. 17 4 mo. 1632; d. at Saconesset, Mass., 12 April 1694; m. (1) ca. 1652 WILLIAM BASSETT, d. at Sandwich, 10 June 1670; m. (2) ca. June 1671 JAMES PERCIVAL, d. at Saconesset, between 19 Jan. and 23 March 1691/2 (John D. Kernan, Percival Genealogy; Preston, Bassett-Preston Ancestors 26, 229). Percival's will is printed in Mayflower Descendant 14 [1912]: 118.
. . ."
Confirms that this William Bassett (of Massachusetts) married Mary Raynesford rather than Hannah Dickerman, who married a different William Bassett in New Haven,Ct.