The USSR was not happy with unauthorised overflights, shooting down everything it could, from spy balloons to U-2s. Also, despite repeated US proposals, something like the Open Skies treaty was only agreed after the USSR disintegration. Nowadays Russia has some ASAT capabilities, but these were being developed during the Soviet time, with a test apparently conducted in 1970.
A (now declassified) US assesment of August 2, 1960 predicted that
Whenever the USSR does acquire a capability, it will probably seek to destroy US reconnaissance satellite vehicles.
So, why did the USSR not try to shoot down US spy satellites?
N.B. I'm aware of the wording of Space Treaty, but this only (kinda) prohibits the shootdown of "peaceful" satellites, which spy ones may or may not qualify as such.
If a State Party to the Treaty has reason to believe that an activity or experiment planned by it or its nationals in outer space, including the moon and other celestial bodies, would cause potentially harmful interference with activities of other States Parties in the peaceful exploration and use of outer space, including the moon and other celestial bodies, it shall undertake appropriate international consultations before proceeding with any such activity or experiment.
Did the Soviets think/interpret that the treaty prohibited the shootdown of spy satellites as well? Or were there more pragmatic reasons?