According to Shoemaker's Ancient Traditions of the Virgin Mary's Dormition and Assumption pp. 68-69, it's from the Euthymiac History:
Perhaps the most famous of these traditions is a brief work known as the Euthymiac History. This legend was interpolated into the second of John of Damascus’ homilies on the Dormition* at an early point in their transmission, where it is identified as a quotation from ‘the third book of the Euthymiac History, chapter 40’. Its inclusion in these, ‘the most celebrated of all the ancient homilies for the feast of the Dormition’, ensured that it was the most widely circulated of the late apostle traditions.150 The Euthymiac History, as quoted in John’s homily, describes an incident that is supposed to have occurred during the events of the council of Chalcedon. While Juvenal[, the Patriarch of Jerusalem,] and the other bishops of Palestine were present for the council, the imperial couple, Pulcheria and Marcian, enquired about the relics of the Virgin Mary, asking that Mary’s remains be sent to the imperial capital, in order to protect it. In response, Juvenal briefly narrates the events of Mary’s Dormition, explaining why there are actually no bodily relics to be had. There is, however, he tells them, another kind of relic that he could send. Three days after Mary’s burial, Juvenal explains, the apostle Thomas finally reached Jerusalem, and, having missed the events of Mary’s Dormition, he requested that the tomb be reopened, so that he might pay his respects (not out of doubt, I might emphasize). When the apostles opened the tomb, they were startled to find no body, but instead only Mary’s funeral robe. Juvenal then concludes by referencing the passage from Ps.-Dionysius’ The Divine Names discussed above, after which the imperial couple requests that Juvenal send them the garment. When Juvenal returns home to Jerusalem, he fulfils their request, and Marcian and Pulcheria enshrined the robe in the church of Blachernae, the Constantinopolitan church that housed this famous relic. It is difficult to date this tradition, and we do not know whether it arose sometime before or after the Islamic conquest. We know only that the legend developed sometime between 550 and 750, making it a potential witness to the earliest development of the Dormition traditions.
*St. John Damascene's homily is referenced in Pope Pius XII's 1950 definition of the dogma of the Assumption, Munificentissimus Deus, §§21-22.