A top National Rifle Association executive signed a document agreeing that the gun-rights organization would be 99% owner of a company formed to buy a $6 million Dallas mansion for NRA CEO Wayne LaPierre, according to a copy of the document reviewed by The Wall Street Journal.

The document also shows the NRA agreed to contribute $6.5 million to the company formed to buy the property, raising yet more questions about the NRA’s previous statements that none of the gun-rights group’s money was to be used to purchase the house...