Is there a connection between Purim masks and the mask Moshe begins wearing at the end of Parshat Ki Tisa? (see Exodus 34:29-35)
It seems too much of a coincidence that it's read near Purim for there to be none.
Seemingly the coincidence might be just that. There is no Halakhic basis for dressing up for Purim nor is it a mesora of all Bnei Yisra'el.
So then the question is if dressing up on Purim does not come from Moshe's mask where and why did this Minhag start? Unfortunately this aspect of the celebration might have a more dubious origin. Dressing up on Purim is a custom that was only found amongst communities in Catholic countries over 100 years ago and coincidentally it has many more similarities with Church festivities then anything found in the Miqra or the Talmud's.
In spring time before the Catholic period of mourning that comes before Easter, a six week period which is traditionally marked by the abstaining of alcohol, fine foods, entertainment of different sorts and with some fasting. Traditionally the eve of Lent festivities include excessive alcohol consumption, food intake other forms of debauchery and most predominately dressing up in costumes and masks to disguise those who are performing such "devilish" activities. These rites of celebration are still preformed around the world under different names: Carnival, Mardis gras, Khamis el sakara, Fat Tuesday etc.
Not only do many communities of Mizrahim, Chabashim and other non-European ethnic groups not dress up on Purim because its not their minhag but many Haradim (of all ethnicities) do not because of the questionable origins of the custom and that partaking in it might constitute breaking the Halakha :
"We may not follow the statutes of the idolaters or resemble them in their [style] of dress, coiffure, or the like, as [Leviticus 20:23] states: "Do not follow the statutes of the nation [that I am driving out before you]," as [Leviticus 18:3] states: "Do not follow their statutes," and as [Deuteronomy 12:30] states: "Be careful, lest you inquire after them." [All these verses] share a single theme: they warn us not to try to resemble [the gentiles]. Instead, the Jews should be separate from them and distinct in their dress and in their deeds, as they are in their ideals and character traits. In this context, [Leviticus 20:26] states: "I have separated you from the nations [to be Mine]."Hilkhoth Avodah Zarah 11:1
There are also many great articles to be found online about this subject written by well learned Hakhamim.
Hope that helps.