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This is actually a common configuration in many parts of the country. A gas furnace with force air heat and an electric AC (electric cooling), commonly called a split system. I have that exact configuration in my house.
I also had a house with central heat in the main part. But the finished attic that didn't have ducts had electric heat, so it's possible something weird-ish like that is going on. But, yeah, the suggestions above seem more likely.
This is an incredibly common setup here in the northeast. As all A/C does, your cooling uses electricity. Your heating system uses either natural gas, propane, or oil. Electric heat is pretty rare around here because it tends to be more expensive than n-gas/propane/oil.
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