Original deed for a renovated 1926 house that HCAD is calling new construction?

Our house was originally built in 1926, then renovated in 1996.

HCAD only has reference to the renovation, which they're calling "new construction." They say that in order to have it revised as a 1926 house with a 1996 renovation, we need a copy or photocopy of the original deed. The previous owner (who did the 1996 renovation) says they don't have that documentation.

Is there a way to obtain the original deed? It doesn't appear in HCAD's records. Are there other Harris County records that it might appear in?