When the Families of Ancient New Haven was published in the 1920's, D L Jacobus, included the family of Gershom Hale. He acquired the family information from Charles R Hale, another noted genealogist. They included two daughters:
Hannah, b. 10 Oct 1680, d. 13 Mar 1724 ae 43 ; m. Joseph Smith
Ann b. 5 Jan 1681/2
Thirty years later, Jacobus published Hale, House and Related Families This contains a different scenario, one daughter.
Ann [Hannah] b. 5 Jan 1681/2, who married Joseph Smith etc.
Needless to say this causes some confusion.
An alternate date of 10 Oct 1676 Concord, Middlesex, Massachusetts, given by the Family Data Collections and such compilations is actually Hanna Held d/o John Held and Sarah born 10 Oct 1676. Because of the similarity of dates, this may be where Hale made his mistake.
About 1681 was used by Jacobus in the Joseph Smith genealogy in Families of Ancient New Haven. This was based on her age at death, 43, given on her tombstone.
Note ?: Are there any records that call her Hannah?
"Ann daughtr of Gershom Heald. born 5.11. 81 (5 Jan 1681/2)
Annah Hale married Ensign Joseph Smith on 30 Dec 1702 in New Haven, Connecticut. 
Ann Smith died 13 Mar 1724, ae 43, in West Haven, New Haven, Connecticut, where she is buried in the Old West Haven Green Cemetery
Children of Hannah and Joseph born in New Haven:
Ann b. 11 Oct 1703 d 26 July 1788; m Japhet Benham
Joseph b. 23 Jan 1705, d 20 may 1776; m. Ester Ives.
Peter b. 11 July 1708; d. 1758; m Elizabeth Hale
Esther, daughter of Ensign Joseph Smith, b. 16 Feb 1711; d. 17 Oct 1725 ae 15
Nathan b. 1 Mar 1713; d. 12 Apr 1787; m (1) Rachel Painter; m. (2) Hannah Trowbridge
Gidion b. July 1720; d without issue 6 Dec 1776; considered incompetent
Benjamin bp 22 Mar 1723/4 ; d 18 May 1792; m. Abigail Smith
↑ 1.01.11.21.3 Donald Lines Jacobus, Families of Ancient New Haven ([CD]Baltimore, Genealogical Publishing Co., Inc., 1981[originally]Rome, N.Y. and New Haven, Conn., 1922-1932), vol 3, p 692. Section on Gershom Hale. Jacobus acknowledges someone else.
↑ 2.02.12.2 Jacobus, Donald Lines, et al., Hale, House and Related Families, Mainly of the Connecticut River Valley (Hartford: Connecticut Historical Society, 1952) p. 263
↑ Edmund West, comp.. Family Data Collection - Births [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2001.
↑Concord, Massachusetts: Births, Marriages, and Deaths 1635-1850. Printed by the Town about 1891. p. 19
↑Families of Ancient New Haven, Vol I-VIII. and Index Vol IX New Haven: 1931. Reprint, Baltimore: Genealogical Publishing Co., Inc., 1974, 1981, 1997. Originally published as New Haven Genealogical Magazine, Volumes I-VIII. Rome, NY and New Haven, CT 1922-1932. p. 1621
↑Concord, Massachusetts: Births, Marriages, and Deaths 1635-1850. Printed by the Town about 1891. p. 25
It may be possible to confirm family relationships with Ann by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share DNA with Ann:
Hale-32 and Heald-5 appear to represent the same person because: Note: Death date for Heald-5 noted as probably fictional....appear to be same person who should have LNAB as Heald in conformation with parents, info about Hale-32 should be transferred to new Heald profile including marriage. Please research before merge if possible. Thanks! Dorothy C