Yes, rental improvements should be depreciated since they improve the life of your rental over several years.  Therefore, you would take a portion of the depreciation each year as you use the improvements.  

Please see the link below for more details on how this process works.  You will also see the steps to report this in TurboTax in the link.

Rental property capital improvements

Can I just enter one entry as a remodel for $12K under assets?

Yes. Since you have only one bill for everything including the painting, that pretty much confirms your painting was "a part of" the property improvements. Just enter everything as one item (assuming it's all placed in service on the same date) in the assets/depreciation section, classify it as residential rental real estate, and it gets depreciated over the next 27.5 years.

Thank you.  The cost would be $12K correct when it asks the amount you paid for it? Then do I select "I purchased this asset new"? 

Yep. For "almost" any asset classified as residential rental real estate, it's purchased new. Your cost basis includes the cost of the materials, installation and labor, shipping, permits, and any other costs associated with the property improvement.