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In a small bowl, whisk together white rice flour, sweet rice flour, and salt.
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Fit stand mixer with flat paddle attachment. In bowl of stand mixer, cream together butter, sugar, and vanilla on medium speed until a thick paste forms and mixture lightens slightly, about 90 seconds. Add dry ingredients and mix for 30 seconds. Mixture will be dry and crumbly.
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Stop mixer and scrape down bowl. Turn mixer back on to medium speed. Mix until a dough forms, about two minutes.
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Lightly spray 11-inch tart pan with non-stick cooking spray. Turn dough into prepared pan. Using your hands, press dough evenly into bottom and sides of pan. Prick dough all over with a fork.
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Cover pan with plastic wrap and chill for two hours.
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Preheat oven to 375°F. When oven is preheated, remove tart pan from refrigerator. Pierce bottom and sides with a fork. Bake until golden brown, about 20 minutes. Remove pan from oven and place on wire rack to cool.