If you are taking the home office deduction and this is a room A/C for the office space and it is less than $2500, you can expense it. If it is a room A/C for non-office space, you can't take anything. If it is the whole house A/C/heat system, and the cost is more than $2500, you depreciate it as a business asset over 20 years. You take the depreciation deduction based on the square foot percentage. Turbotax should allow you to enter the item as an improvement to the home that is subject to depreciation.
If the total cost is more than $2500 but the business share is less than $2500, you might qualify to use the $2500 safe harbor to expense it all at once, I would expect turbotax to let you know.
And, any part you expense or depreciate for the home office reduces your cost basis in your home must be used to reduce the amount that the improvement otherwise increases the value of your home.
