As noted in the comments, there's nothing in the song that's explicitly about Passover, but there are a few lines with themes that might relate thematically to Passover. In the original version it says:
Eight candles shine for the Maccabees.
Eight candles shine for the Maccabees.
Down from the mountains with Liberty's sword,
They came like the flame of the Lord.
Chorus:
Dance the horah,
Light the menorah,
This is the time of joy.
The road to freedom we take today
With the Maccabees leading the way.
Eight candles shine for the Maccabees.
Eight candles shine for the Maccabees.
The tyrant was routed with all of his men,
And the temple made holy again.
(Chorus)
Eight candles shine for the Maccabees.
Eight candles shine for the Maccabees.
Hanukah's children will never forget
The glory that shines for us yet.
The lines "Down from the mountains with Liberty's sword" and "The road to freedom we take today" are related to the theme of Passover of being freed from servitude.
The line "The tyrant was routed with all of his men" is thematically similar to a verse that appears in Exodus 14:28 when God drowned the Egyptians in the Sea of Reeds:
"The waters turned back and covered the chariots and the riders—Pharaoh’s entire army that followed them into the sea; not one of them remained."
as well as a verse in the next chapter, in the Song of the Sea, which was sung by the Israelites after the Egyptian drowned in the Sea of Reeds (Exodus 15:4):
"Pharaoh’s chariots and his army
He has cast into the sea;
And the pick of his officers
Are drowned in the Sea of Reeds."
In both cases (Reynold's song and the biblical verses), we find the idea of the utter decimation of an evil king and his army.
If you really want to stretch it, you could tie the "Dance the Horah" line to the celebratory dances of the Israelite women (Exodus 15:20):
"Then Miriam the prophet, Aaron’s sister, picked up a hand-drum, and all the women went out after her in dance with hand-drums."
But pretty much everything in the song is already connected in ancient sources to the actual story of Chanukah (except maybe the dances, but it's very likely that something of the sort did occur), so there doesn't appear any real reason to see part of the song as directly referring to Passover. Unless, of course, Reynolds stated somewhere that she based the song off of the Passover story or the festival in general.