A purely speculative post; I am not a medieval historian or linguist, and this is just something I’ve noticed whilst reading A Lytell Geste of Robyn Hode (1510). I may be wrong, and am certainly willing to be corrected; comments are most welcome!
It is generally agreed amongst most major Christian religions that Jesus Christ died on a cross; an upright stake with a crossbeam. That Christ died on a cross, however, has been debated over the centuries, and some early-modern scholars such as Justus Lipsius illustrated the different ways in which a crucifixion could be carried out. In particular, his illustration of the crux simplex in De Cruce Libri Tres (1594) shows a man suspended upon an upright stake,  indicating that the instrument of death used to torture Christ could have been a simpler device compared to the cross that is commonly accepted in many Christian religions,  although Lipsius does also include illustrations of more recognisable crucifixions carried out upon a standard cross. Even in the modern period Patrick Fairbairn in The Imperial Bible Dictionary (1874) suggested that the ‘cross’ which Christ died upon may originally have been an upright pole. 
It is not the intention here to debate whether or not Christ actually died upon an upright stake, but to highlight a surprisingly interesting source where it appears as though it is implied that Christ died, not on a cross but upon a tree. This source is the medieval ballad A Lytell Geste of Robyn Hode. No precise date can be given for the original composition of this ballad as it is a compilation of a number of Robin Hood tales that were originally disseminated orally,  although somewhere between c.1400  and c.1450  seems to be the consensus among researchers. The first printed appearance of the Geste, however, appeared in 1492, with successive editions appearing throughout the sixteenth century.  The Geste then made its appearance again in eighteenth-century ballad collections such as Joseph Ritson’s Robin Hood: A Collection of All the Ancient Poems, Songs, and Ballads (1795), and Francis James Child’s five-volume work English and Scottish Popular Ballads (published between 1882 and 1898). It is a long tale composed of eight ‘fyttes’ and sees Robin and his men relieve a financially distressed knight; participate in archery contests; meeting with the King; and the Geste also tells of Robin Hood’s death at the hands of the Prioress of Kirklees.
It is in Robin’s meeting with the poor knight in the first fytte that the first reference Christ dying upon a tree is found. Robin asks the knight why he is poor. The knight has had to post bail for his son who slew a man of Lancaster, and to get the needed funds he has had to mortgage his lands to the corrupt abbot of St. Mary’s in York. When Robin meets the knight, it is the day that the repayment is due, the funds for which the knight does not have. And neither does the Knight have any friends who can help him out of his financial difficulties:
Hast thou ony frendes sayd Robyn
The borowes that wyll be
have none then sayd the knight
But god that dyed on a tree. 
Robin lends the knight the £400 that he needs to repay the abbot, and sends the knight on his way to York with Little John acting as a man-servant. When John and the knight arrive at the Abbey of St. Mary’s, the knight initially pretends that he cannot repay the loan. He initially pleads for mercy from the abbot, but to no avail for the abbot refuses to show any leniency:
The abbot sware a full grete othe
By god that dyed on a tree
Get the londe where thou may
for thou getest none of me. 
To the abbot’s chagrin, the knight reveals that he does indeed have enough money to repay the abbot, and that if the abbot had been willing to show courtesy and mercy towards him, he would have been rewarded. The abbot turns to the justice who is in the room and says:
Take my golde agayne sayd the abbot
Syr justice that I toke the
Not a peny sayd the justice
By god that dyed on a tree.
Whoever the anonymous author(s) of the Geste was, it is clear that he is here referring, not a cross, but to a more simple structure. When the Sheriff of Nottingham sees Little John’s archery skills on display at a shooting match, he makes a similar oath ‘by hym that dyed on a tree.’ There is also another similar reference later on in the ballad. After an archery contest in Nottingham, when Robin splits the arrow in two, the Sheriff recognises them and the outlaws rush to make their escape. In the ensuing affray Little John is wounded, and he asks Robin:
Mayster then sayd Lytell Johan
If thou ever lovest me
And for that ylke lordes love
That dyed upon a tre
And for the medes of my service
That I have served the
Lete never the proud sheryf
Alyve now fynde me.
Now it might be thought that too much is being read into these passages, and I could just be splitting hairs (feel free to comment below). After all, a tree can indeed mean a cross. The only time that the author uses a variation of the phrases previously highlighted is at the end of the eighth fytte where it says:
Cryst have mercy on his [Robin’s] soule
That dyed on the rode.
According to the Middle English Dictionary Online, the word ‘rode’ can mean ‘cross’ in the term by which it would be popularly understood. It remains to ask, however, why the author, or authors, of the Geste used ‘tree’ throughout the ballad when there were words which would have more clearly conveyed the sense of a cross proper?
 Justus Lipsius De Crvce Libri Tres Ad sacram profanamque historiam utiles. Vna cum Notis (Antwerp: 1594), p.10.
 The exception to this is the Jehovah’s Witnesses’ religion. They believe that Christ died upon an upright stake, or pole with no crossbeam. Their position is explained in one of their society’s publications. See Anon. Insight on the Scriptures (New York: Watchtower Bible & Tract Society, 1988), pp.1116-1117. [See jw.org]
 Patrick Fairburn The Imperial Bible Dictionary (London: Blackie & Son, 1874), p.376.
 Stephen Knight Robin Hood: A Mythic Biography (Ithaca: Cornell University Press, 1994), p.24.
 A. J. Pollard writes that ‘textual and linguistic analysis has suggested a possible date of composition of the elements [of the Geste] as early as c.1400 and dates for the compositions to be committed to writing about 1450. See A. J. Pollard Imagining Robin Hood: The Late Medieval Stories in Historical Context (London: Routledge, 2004), p.6.
 There is debate about the dating of A Lytell Geste of Robyn Hode, but James C. Holt argues that c.1450 was a ‘safer date’ than c.1400. See James C. Holt, ‘Robin Hood: The Origins of the Legend’ ed. by Kevin Carpenter Robin Hood: The Many Faces of that Celebrated English Outlaw (Oldenburg: Bibliotteks- und Enformationssystem der Universität Oldenburg, 1995), pp.27-34.
 Pollard, Imagining Robin Hood, p.6.
 Anon. Here begynneth a Lytell geste of Robyn hode and his meyne And of the proude Sheryfe of Notyngham (London: Wynken de Worde, c.1510) Cambridge University Library Shelfmark: Sel.5.18 S.T.C. No. 13689
 Frances McSparran (ed.) Middle English Compendium (University of Michigan, 2006) [Internet <<http://quod.lib.umich.edu/m/mec/index.html>> Accesssed 14/08/2015].