R' Yaakov Elman has done a lot of work on the subject.
(See his article "Acculturation to elite Persian norms and modes of thought in the Babylonian Jewish community of late antiquity" in Netiot L' David - Prof. Dovid Halvni's Festschrift (which I happened to have read while sitting next to Prof. Halivni. I ought to have asked him of his opinion on the subject while I was there - Chaval Al D'Avdin.) See also his article in Printing the Talmud which is online.)
There is a full dissertation on the subject:
"Dashtana -- 'ki derekh nashim li'": A study of the Babylonian rabbinic laws of menstruation in relation to corresponding Zoroastrian texts
by Secunda, Samuel Israel, Ph.D., Yeshiva University, 2008, 502 pages (Advisor:Y. Elman)
This is the abstract:
For over half a century, academic scholarship of the Babylonian Talmud (Bavli) has focused primarily on the dynamics of this work's internal textual (lower and higher criticism) and hermeneutical phenomena. This dissertation participates in a recent scholarly endeavor to consciously incorporate the Bavli's external, Sasanian Iranian context into talmudic research. By closely examaning the development of the Babylonian rabbinic laws of menstrual purity ( hilkhot niddah ) against corresponding Zoroastrian texts, I argue that rabbis and Zoroastrian priests were engaged in similar, sustained legal discussions that reconsidered (a) the role of religious authorities in determining the legal onset of menstrual impurity, (b) whether to delay purification rituals beyond the cessation of the menstrual flow, and (c) the place of menstruants in the home and society. In each of these cases, rabbinic and Zoroastrian sources share analogous legal trajectories that testify to a broader conversation that was taking place in Sasanian Iran. In addition, analysis of seven talmudic aggadic (non-legal) sources reveals a dynamic in which the rabbis were aware of the importance of menstrual purity amongst Persians and anxious about the legitimacy of certain rabbinic menstrual purity practices in light of Zoroastrian stringency. Consequently, the rabbis sought to assert the authoritativeness of the rabbinic system by imagining the Sasanian queen-mother consulting (and subsequently praising) a prominent fourth century talmudic sage in order consulting (and subsequently praising) a prominent fourth century talmudic sage in order to diagnose her bloodstains. In a different passage, the Bavli depicts an important talmudic sage verbally sparring with an anonymous "Zoroastrianized" heretic. The rabbinic sage claims that even spiritually weak Jews are uniquely equipped to withstand the temptations of violating the menstrual prohibitions. Finally, another Babylonian rabbinic sage claims that the Zoroastrian menstrual purity system is actually derived from the Jewish one since the Persian word for menstruation, dastan, can be traced to the biblical matriarch, Rachel. The parallel legal trajectories and the dynamic of rabbinic defensiveness in the face of Zoroastrian stringency all contribute to our understanding of the Bavli and its relationship with Sasanian Zoroastrianism.
Lest we become to carried away finding parallels (This is a general comment. U am certainly not referring to Prof. Secunda's exceelent disssertation.) it is worth quoting the following:
We may grant that we meet with Persian influence in the Jewish conception of angels, ritual cleanliness and uncleanliness, and in a few ethical sayings, etc. On the other hand, we can be certain that Persian business law did not influence the Jews; for the latter never came in contact with it!
The Relation of Jewish to Babylonian Law Author(s): H. S. Linfield Source: The American Journal of Semitic Languages and Literatures, Vol. 36, No. 1, (Oct., 1919), pp. 40-66
[As Prof. Secuda comments: "In any case, Linfield's comments from 1919 were made before significant work had been done on Sasanian civil law - which is collected primarily in a seventh century work, "The Book of a Thousand Judgments." See Elman's JSIJ article for an example of rabbinic discussion of Sasanian civil law.Of course in all of this we need to remember that the Bavli is built upon Palestinian material which is then (re)interpreted and (re)applied to new realities. uncovering so-called "Persian influences" is not just a matter of finding similar sounding laws in Zoroastrian texts, but of looking for simialr trajectories and the like."
Elman's JSIJ article can be found here. Certainly, the Persian Law influeneced the Talmudic law, in the same way that American law might affect an American Posek's Teshuvos. But it is only in the issues of magic,etc. that Zorastriansim would be the source for the Talmudic statement.]
See also Encycylopedia Iranica s.v. Talmud