Drum heads, historically, were made out of calf, goat, or sheep skin. The Duke of Norfolk in the 15th century made
payments for repairing instruments - a cord for a tabor (1464) and parchment [4d to the taborets for parchment]
to repair a tabor (1481).
Accounts of the household of Thomas and Edmund, the king’s sons
11d to Martinettus the taborer, for the repairing of drums of the king’s sons and for moneys paid by him for
parchment for the covering of the said drums: London, 18 November.

In the 17th century in France, Mersenne (1636) notes that the heads should be made of sheepskin.

Also… "writing parchment, drum-heads" …etc etc

“Friday last the Glassmakers at Newcastle made a most droll and laughable procession.—
- Their champion and other officers were mounted on asses, …sticks and shovels in place of music,
and empty butter firkins for drums.”

Leeds Intelligencer - Tuesday 10 November 1772

1795 story ‘The Village Assembly’

“…two blind fidlers, and a pipe and tabor, the parchment of which had met with a fraction,
consequently emitted a most horrid report, but every body's oral nerve not being so quick as
mine, it did not appear to affect them. …”

[Ed This passage is followed by a hilarious description of some of the dancers]

'The Observant Pedestrian; or, traits of the heart: in a solitary tour from Cærnarvon to London: in two volumes,
by the author of The mystic cottager. 1795: Vol 2'

1843 new inventions: a case heard in the Vice Chancellors’ Courts [part]:English Chronicle and Whitehall Evening Post - Saturday 11 November 1843

More information on this case in the Morning Herald (London) - Thursday 02 July 1846, pages 6, 7

1896 advert [detail] Derry Journal - Monday 17 August 1896

Newspaper advertisements for sales of drum-heads continued into the twentieth century.

19th century Oxfordshire

“In an old Oxfordshire cottage there still hangs from an ancient beam the Tabor of bygone days, no longer
to set the feet a-going, but to act as a weather prophet by the stretching of its time-worn skin.”

‘Old English Instruments of Music - Their History and Character 1911’ Galpin, Francis W. page 150

1532-1564 story that mentions recycling a legal document written on parchment:

“ … But what harm had poor I done? cried Trudon, hiding his left eye with his kerchief, and showing his tabour
 cracked on one side: … they have also broke my harmless drum. Drums indeed are commonly beaten at weddings,
— and it is fit they should; but drummers are well entertained, and never beaten… Brother, said the lame catchpole,
never fret thyself; I will make thee a present of a fine, large, old patent, which I have here in my bag, to patch up
thy drum…”

‘The Horrible and Terrifying Deeds and Words of the Very Renowned Pantagruel King of the Dipsodes,
Son of the Great Giant Gargantua’ by François Rabelais, chapter 12
Great books of the Western World by Encyclopaedia Britannica, pub 1986

England, cases heard at The Old Bailey, London and in the newspaper:
6th September 1693
“John Redshaw was arraigned for stealing a parcel of Parchment Writings, value 200 l. from one John Day
on the King's Highway, but no Evidence coming against him, he was acquitted .”

17th January 1739
"124. of London, Gent . was indicted, for that he, on the 28th of October , &c. with Force and Arms,
in the Parish of St. Dunstan in the West , did feloniously steal, &c. a certain Parchment Writing, … 
the large Pieces the Witness's Wife sold at a Turner's Shop, to make Drum-heads. …"

1739 theft of parchment, trial account:
  “Gent… did feloniously steal, &c. a certain Parchment Writing,…the Prisoner often came into that Office,
and into the Record-Room, and frequently made use of those Opportunities to take away a great Number
of Records, Bills in Chancery, Answers, and Commissions issued out of Chancery to assign the Bounds
of Manors, &c… the next Use was, to dispose of the Parchments themselves, which he did to various
Persons in various Employments: … one Lulham, a Confederate with the Prisoner, made a Discovery
before the Lord Chief Justice of the King's Bench, of his having at various Times received many of these
Records, sold the Stamps, and dispos'd of the Parchment, to make Glew, Drum-Heads, and Taylors
Measures, &c. &c”

Proceedings of the Old Bailey, 17th January 1739, t17390117-45

1816 “CHARLES RICHARD HURD and RICH-ARD KILMINSTER were indicted for stealing,
on the 6th of November one hundred pounds weight of parchment, value 5l
I have the care of the bills and answers at their office. In the month of November last, I missed four bundles
of bills and answers, and twenty three bundles of replications. I suppose I missed from one to two hundred
weight. I know the two prisoners by their being writers in the office. They are father and son-in-law.
In consequence of some information, I went to Mrs. Bridges, Drum-maker, at Hoxton, on the last day of February.
I found there a great quantity of the parchment which I had lost, made up into drums and tambarines. 

1834 theft of parchment, trial account:

 EDWARD GRAY and WILLIAM SHELLEY were indicted for stealing, on the 20th of November,
5lbs. of parchment, value 1s. 6d.
“police-constable G 145: I saw the two prisoners—Shelley had a bundle under his arm—I asked what it was
—he said some parchment which belonged to that young man, (pointing to Gray who was behind him,) and it
was some that his master had given him… Shelley said it was some that Gray bought of his master, that he had
given it to him to carry, and they were going to Whitecross-street, to sell it to a drum-maker”

Proceedings of the Old Bailey, 24th November 1834, t18341124-149

The British Columbia Folklore Society writes in 2023:

“The parchment sides—one of which is fitted with a snare, should, we are told, be cut from an old will or testament,
because the skins upon which these were engrossed were peculiarly resonant!”