In regard to the cost basis for my house is that calculated from the original purchase or when it was refinanced?

The original cost/purchase price.   The Mortgage or refinance doesn't figure into it.  

It’s computed from your original purchase.

The adjusted cost basis of your home is the original price you paid, plus the cost of any capital improvements  that you've made since purchase.  Refinancing isn’t part of your calculation.

A capital improvement is any work done that adds to the value of your home, increases its useful life, or adapts it to new uses.  Common examples include room additions, new bathrooms, decks, fencing, landscaping, wiring upgrades, walkways, driveway, kitchen upgrades, plumbing upgrades, new roofs.

The adjusted basis of your home is the original purchase price, plus certain settlement fees paid at time of purchase, and the cost of any improvements made to the home prior to your sale.

For a detailed explanation of items that can be added to your original basis to arrive at your adjusted basis, please see IRS Publication 523, Selling Your Home.

@VolvoGirl, I thought costs associated with purchasing the property (like title search fees or recording fees) are added to the property's cost basis. Is that the case only when purchasing the property or also when refinancing the loan related to the property? 

Cost basis =  purchase price + cost to buy + improvements