The frame
The Met's timeline page for Mesopotamia, 2000-1000 BCE, gives this period the label "Late Bronze Age", about 1600-1200 BCE. In the north it lists the Mitanni period, about 1600-1350 BCE, followed by the Middle Assyrian period, about 1350-1100 BCE; in the south the Kassite dynasty, about 1574-1157 BCE, and the Middle Babylonian period, about 1400-1100 BCE. According to the page's events for 1600-1350 BCE, artistic motifs and styles travelled across the Near East on portable items such as ivories and seals, and at the Egyptian capital at Amarna an archive including cuneiform letters was found. Source 1.
Boundaries and overlaps
Three of the listed periods do not end at 1200: the Kassite dynasty lasts until about 1157 BCE, and the Middle Babylonian and Middle Assyrian periods until about 1100 BCE, while the "Iron Age" begins, on the same page, from about 1200 BCE. The Middle Babylonian period begins about 1400, within the time of the Kassite dynasty, so the two southern entries overlap. The event that describes the Kassite kudurru, a stone that according to the page was used to record royal grants, is also dated about 1350-1000 BCE and crosses the boundary. The site keeps 1200 as the boundary and places each item by its own dated phase. Source 1.
On this site
One article is placed in this period: "Nuzi: the archive of a medium-sized town in the Mitanni kingdom", on a town that according to a Harvard Art Museums record was destroyed about 1350 BCE and yielded more than 8,000 tablets and fragments. It is the only item, so the period is marked as a gap. The Louvre record of the kudurru of Nazi-Maruttash was also checked, and it contradicts itself: its date-of-creation field reads "2nd half of the 14th century BCE", 1307-1282 BCE, the reign of Nazi-Maruttash, the king who granted the land; but the description in the same record says that the stone is a copy made "several generations later" under Marduk-apla-iddina I, with no date for the copy, and that it was carried to Susa as booty in the 12th century BCE. The record therefore dates the grant, not the stone itself, and the stone is not placed in this period. Missing: a second item, for instance a Kassite or Middle Assyrian object, whose source dates the object itself, or an excavated phase, to about 1600-1200 BCE. Sources 2, 3.