Number of persons and identity of crew members of the
English Navy's armed schooner GASPEE.

The six sloops/schooners purchased by the English Navy, of which the Gaspee was one, were each authorized to maintain a complement of 30 men.  The officers and some crew came from England; some of the crew were impressed or enlisted from the American or Canadian colonies.

In June, 1772,  the full ship's complement of personnel of the Gaspee consisted of the "captain" (a Lieutenant, because the size of the ship did not warrant a person with the English Navy rank of captain being in command),  a midshipman, a master, 22 sailors, and a local pilot (because of the rivers and harbors and bays that had to be patrolled.

On the night in question, June 10, 1772, the pilot had been released from his job for some unknown reason and the "Master and four men were gone on duty to Boston with a Vessel which we had seized." This left on board on the night of the attack only its authorized two officers (Lt. Dudingston and Midshipman Dickinson) plus "about 19 ' crewmembers according to the crew's depositions at the later court martial of Dudingston. 

The Gaspee.org site has retrieved documents from the English archives and has found the master pay list for His Majesty's Schooner Gaspee, for the full time of her existence from Dec 1763 to June 1772.  Over her 106 month existence, The Gaspee had over 230 crewmen.  Over that 106 month existence 142 (62%) deserted the ship, and 8 (4%) died at one point or another.  John Concannon has identified from that pay list, the following men as probably being in the crew of the Gaspee on the night of the attack against it. (His identification is one short of the "about 19" testified to by the crew.)
 

Officers (including masters and midshipmen)

Lieutenant William Dudingston (31), Captain (Listed in ship's papers as "Lieut & Commander")  Dudingston was first commissioned in the Royal Navy as a Lieutenant on 10 Oct 1759. His first command was that of the Gaspee schooner on 13 Sep 1768. Thus he had been on the same ship, on a customs enforcement assignment, for some time before arriving in Narragansett Bay. 
James Dundas (ca. 27), "Second Master & Pilot." The "master" of a navy ship was mainly in charge of operating the ship and was not necessarily an officer. In practice a master often functioned as junior in command to the officers and midshipmen, and was sometimes charged with leading missions ashore or commanding boarding parties.  After the seizure of the ship Fortune, the master of the Gaspee was in charge of the four Gaspee crewmen sailing the Fortune to Boston for legal proceedings there.  Because after the Gaspee he was given command of his own ship [Captain "Prime" 1772/3, appointed 18.8.1772 age 28,1776/7, 1778/9], we have placed him above Dickinson in the Gaspee's order of command.
William Dickinson (31),  Midshipman.  A person desiring to be an officer in command of a ship had, by English Navy regulation, to serve at least two years as midshipman on a vessel. The midshipman was the lowest rank of officer, entitled to a salute, but only called "Mister".

Mates

1. John Johnson,  Boatswain's Mate. (the ranking seaman)
2. Joseph Bowman (46), Gunner's Mate.
3. John Phillips,  Acting Surgeon's Mate.

Seamen

1. Edward Brown (21), from Orkneys, Scotland
2. William J. Caple (33), from Munster, Ireland.
3. Bartholomew Cheever (36), from Boston. MA.
4. Timothy Dunavan (25), from Kinsale, Ireland.
5. Patrick Earle (28), (aka Paddy Alis), from Cork, Ireland
6. James Edwards (21), from Bristol, RI
7. Francis Hussay (21), from Lisbon.
8. John Keaton (25), from Cork, Ireland.
9. Richard Kent (22), from Cornwall, England.
10. Robert Lane (27), from London. Clerk.
11. Robert Masters (25), from London.
12. Peter May (25), from London.
13. John Montgomery (22), from Londonderry, Ireland.
14. Thomas Parr (24), from Lancaster, England.
15. Patrick Phalen (23), from Cork, Ireland.
16. Edward Pullibeck (22) from Modbury, Devonshire.
17. Patrick Reynolds (21), from Londonderry, Ireland.
18. Charles Short (24), from Falmouth, MA.
19. Thomas Totten (21), from Belfast, Ireland.

Local Pilot

In the Bay Area, the Gaspee also hired from time to time a local pilot who knew the waters of the specific area.  Narragansett Bay had so many inlets and indentations et cetera, that it was prudent to do so.  However, the local pilot was not on board when the Gaspee went aground in June, 1772.

Central testimony re numbers of English Crew aboard at the time of the attack.

The testimony at the court martial of Lt. Dudingston included some testimony about the number of crew members of the Gaspee.