Form 5695 Energy Home Improvement Credit Joint occupancy. Do I need to select joint occupancy eventhough I 100% paid for the furnace cost?

No, you do not need to select joint occupancy.  On Form 5695, the instructions indicate to check the joint occupancy box if you shared the home and the costs of improvements.  Since you did not share the costs, the box isn't applicable.  If you did check the box, the credit will still be figured allocating you 100% of the cost since you paid 100% (the numerator is the amount you paid and the denominator is the total amount paid by you and all other occupants).