When taking the first measurement, arterial blood pressure should be taken on both arms. If there is a significant difference, later measurements should be taken on the arm with the highest values.
Apart from this special case, we often suggest, as a convenience for self-measurement, to place the cuff on the left arm for right-handed people and vice versa. Once the side for taking measurements has been chosen, all measurements should be taken on the same arm.
*credit to Sylvain of iHealth Labs EU