In the very first measurement, the blood pressure should be measured on both arms. If there is a significant difference, subsequent measurements should be made on the arm where the highest value has been observed.
Apart from this particular case, it is generally advisable, as a convenience for self-measurement, to place the cuff on the left arm for the right-handed ones and vice versa. Once the side of the measurement has been selected, all measurements must be taken on the same arm.
*credit to Sylvain of iHealth Labs EU