In The Midrash Says Vayikra page 32 the author writes that the chatas nasi was brought by a Jewish king or Head of the Sanhedrin who sinned. Is this correct, and if so is there any source for it? I was under the possibly mistaken impression that only a King brought a chatas nasi.
Mishnah Horayos 3:3:
וְאֵיזֶהוּ הַנָּשִׂיא, זֶה הַמֶּלֶךְ, שֶׁנֶּאֱמַר (ויקרא ד) וְעָשָׂה אַחַת מִכָּל מִצְוֹת ה' אֱלֹהָיו, נָשִׂיא שֶׁאֵין עַל גַּבָּיו אֶלָּא ה' אֱלֹהָיו
Who is meant by a ruler? A king; for it says, “Any of all the commandments of the Lord his God” (Leviticus 4:22), a ruler (king) who has none above him save the Lord his God.
The deresha used implies that the requirement of Nasi is anyone at the top of societies' hierarchy - not necessarily a king.
Gemara Horayos 11b
בעא מיניה רבי מרבי חייא כגון אני מהו בשעיר אמר ליה הרי צרתך בבבל
Rebbi (Yehuda Hanasi) asked R' Chiya - someone like me, would he bring a goat? He said to him, "Your superior is in Bavel".
As Rashi explains, were it not for the Exilarch in Bavel being superior to Rebbi, he would, despite not being a "king", have brought a korban nasi.
It's clear from the *Gemara *that any "head" would be a nasi for the purposes of the korban, as long as they are actually supreme.
The Gemorah then quotes a different version of Rebbi's question:
רב ספרא מתני הכי בעא מיניה רבי מרבי חייא כגון אני מהו בשעיר א"ל התם שבט הכא מחוקק
התם שבט - דהיינו מקל כמו כי תכנו בשבט לא ימות והכא מחוקק - חכם
Rashi here explains that political power (a staff in the sense of a weapon) is required, not just being a teacher of law.
This second version implies that Rebbi was intrinsically excluded from nasi-hood, as he lacked the necessary political power (I assume being subservient to Roman governors).
However any leader with supreme political power, whether king or not, would be included. The nasi of the Sanhedrin may at times have held such power, and it's probably that type of leader which the book you quote refers to.