I recently wrote an answer about Achaemenid primary sources. I didn't link all of the links I have for the Persepolis Archives in that post, but I can post them here because they will probably be the most important sources for your paper. That said, other examples like the Daiva Inscription of Xerxes, the Behistun Inscription, and the Cyrus Cylinder all of interesting implications for Persian law. So far as I know, we don't have any written record of an Achaemenid Persian law code. You might also find interesting implications about law in the older portions of the Zoroastrian Avesta, but will have to be cautious with that because we know so little about actual Achaemenid religion. Persepolis Links:

• “Persepolis Fortification Tablets,” Richard T. Hallock, 1969.
• “Persepolis Treasury Tablets,” George G. Cameron, 1948.
• “Aramaic Ritual Texts From Persepolis,” Raymond A. Bowman, 1970.
• “Administrative realities: The Persepolis Archives and the archaeology of the Achaemenid heartland,” W.F.M Henkelman, 2013.
• The Achemenet article and bibliography of Fortification Archive publications.
• The Achemenet gallery of Fortification Tablet photos.
• University of Chicago PFA Project website.
• University of Chicago PFA Project Annual Report Feed

The Persian Empire: A Corpus of Sources from the Achaemenid Period by Amelie Kuhrt is also a good compilation of primary sources from and related to the Achaemenids. The culture and social institutions of ancient Iran by Muhammad Dandamaev and Vladmir Lukonin is also an under appreciated secondary source that you would probably find very useufl with your topic.

I'm not really the best person to ask for Assyrian sources. Livius.org has many of the Mesopotamian chronicles from the Sumerians to the Parthians, including Assyria, and cites the compilation of translations that they used for each one. Fordham University's Internet History Sourcebooks has some Assyrian documents in translation. That even includes an Assyrian law code. I've never personally used this last one, but I also bookmarked this catalog that you might find useful a while back from Jstor.

For Assyria, begin with the State Archives of Assyria, which has made translations of letters, treaties, decrees, land grants, etc. available for free online. The SAA volumes do not include royal inscriptions, however, which have been published in the Royal Inscriptions of the Neo-Assyrian Period (RINAP) volumes, some of which are also available online.

A Companion to Assyria edited by Eckart Frahm has several chapters on Assyrian administration and law. The King's Magnates by Raija Mattila is very useful as well, although I don't know if you'll be able to find a copy with most libraries closed. Law Collections from Mesopotamia and Asia Minor edited by Martha Roth is the standard set of translations of laws from the ancient Near East, and the best commentary on ANE law is A History of Ancient Near Eastern Law edited by Raymond Westbrook.

Finally, be sure to check out the UCL page on the governance of the Assyrian empire and Karen Radner's free online course Organising an Empire: The Assyrian Way.