The text below is taken from the peace treaty between Japan and the Allied Powers signed in 1951:

All occupation forces of the Allied Powers shall be withdrawn from Japan as soon as possible after the coming into force of the present Treaty . . . Nothing in this provision shall, however, prevent the stationing or retention of foreign armed forces in Japanese territory under . . . bilateral or multilateral agreements which have been or may be made between one or more of the Allied Powers, on the one hand, and Japan on the other.

Source: http://www.taiwandocuments.org/sanfrancisco01.htm

The Soviet Union refused to sign this document. What would have been their objection to the treaty?

The Soviets did not agree to withdraw their forces from Japan.
Japan would not agree to a bilateral agreement with the Soviet Union about stationing forces there.
The Soviets claimed that the treaty would allow the United States to maintain missile sites in Japanese territory.
Japan requested that the Soviets withdraw from the Korean peninsula.