Author Gale Ion Harris in the article "The Doubtful English Ancestry of Richard Smith of Wethersfield,"  says this Richard and Rebecca may have also had children Anne Smith bp 24 Feb 1621; and Rebecca bp 11 Dec 1630 that probably died young as there is no record of them in New England.
... Richard Smith, b. say 1583 [footnote: Aged "about 84 years" on 2 February 1666/7 ("Medical Records of John Winthrop," Manuscript, 701, ... cited by Gale Ion Harris [footnote: See Jacobus, "Richard Smith of Wethersfield", The American Genealogist 25:126, for the 1669 reference to him "come 80 years."].
Harris, in the Register article cited, indicates that the 1669 entry actually reads 'above 80 y', and uses a birth year of about 1583, based on the 1666/7 reference giving his age as 84.
In 1949 Donald Lines Jacobus identified the wife of Richard Smith of Wethersfield, Connecticut as Rebecca Buswell . Roderick Bissell Jones, "The English Ancestry of Richard Smith of Wethersfield," published in NEHGR 128:136-139, identified Richard Smith as the man baptized 16 November 1585 at Stratford-on-Avon, co. Warwick, and traced family relationships for that man. Later Dr. Gale Ion Harris cast doubt on this identification in "The Doubtful English Ancestry of Richard Smith of Wethersfield, Connecticut," NEHGR 143:240-246. Thompson's research has confirmed that Richard Smith of Wethersfield was married and had children baptized not at Stratford-on-Avon, but in Husbands Bosworth, co. Leicester, where his wife's family lived. Richard Smith's ancestry remains to be established.
Richard married Rebecca Buswell, daughter of Roger Buswell and Margaret Unknown (Buswell), on 13 Feb 1614/15 in Leicester, Eng. (Rebecca Buswell was born in 1593 in Leicester, Eng. and died about 1667 in Wethersfield, Hartford Co., CT.)
Marriage 13 Feb 1615/16, Husbands Bosworth, Leicestershire, England to Rebecca Buswell.
13 Feb 1615.
Parish, Leicestershire, , England. 
Smith, Richard (ca 1589-1669+) & Rebecca [?Buswell] (-1667+); b 1617; Wethersfield, CT.
Donald Lines Jacobus, “Richard Smith of Wethersfield,” . On 21 February 1652[/3], Richard Smith wrote from Wethersfield to John Winthrop Jr. in New London describing the strange symptoms of “[m]y sons wife Lidia Wright,” who was suffering from an ailment modernly diagnosed as pulmonary echinococcosis (Malcolm Freiberg, ed., Winthrop Papers, Volume VI, 1650–1654 [Boston: Massachusetts Historical Society, 1992], 251–52, note 3). The editor unfortunately followed confused and superseded accounts in Henry R. Stiles, The History of Ancient Wethersfield, Connecticut, 2 vols. (New York: Grafton Press, 1904; repr. Somersworth, N.H.: New England History Press, 1987), 1:299, 2:645, for remarks about the identity of this Richard Smith.
Lawsuit; 14 May 1652; Hartford, Hartford Co., CT. Richard Smith plt Contra Georg Woollcott and his wife defendts in an Action of Slaunder to the damage of 100£. In the Action betweene Rich: Smith plt and Geo: Woolcott and his wife defendts the Jury findes for the plt damages 28£ and Costs of Courte: Execution dd the 22th of July 1651.
Marriage - Granted Permission; 26 Aug 1657; Hartford, Hartford Co., CT. A Coppy of a Certificate vndr the names of these subscribed: These are to certify to any to whom it may come, that our children John Addams & Abigail Smith haue our full consent to be marryed together, & wee know not engagemt of either party to any other, as wittnesse our hands. Rich: Smith Jer: Addams
Aug 1658, A Petition from several of the inhabitants of Wethersfeild*
↑ 2.02.12.22.32.4 Thompson, Neil D.. "Isaac Buswell and Rebecca (Buswell) Smith of Husbands Bosworth, Co. Leicester, and New England". New England Historical and Genealogical Register. Vol 158 (Jan 2004), p 38. Subscription$
↑ 3.03.13.23.3 Donald Lines Jacobus, "Richard Smith of Wethersfield," The American Genealogist, Vol. 25, 1949, 126-139 pg. 126.
S13 The public records of the Colony of Connecticut ... transcribed and published, (in accordance with a resolution of the General assembly) ... Published 1850 by Brown & Parsons. in Hartford. Covers years 1636-1776. Vols. 1-3 edited by J. H. Trumbull; v. 4-15, by C. J. Hoadly. archive.org
U.S. and International Marriage Records, 1560-1900 Yates Publishing Publication: Ancestry.com Operations Inc
Find A Grave: Memorial #157393648 Wethersfield Village Cemetery. No source. No photo. Wrong death date. No value.
Thank you to all who have contributed to this profile.
It may be possible to confirm family relationships with Richard by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: