Did the CIA follow a documented set of criteria when determining targets for political assassination during the Cold War, especially in regards to foreign heads of state or government? There have been examples from history where the CIA assassinated foreign leaders, "on orders from the White House", but would they have always been blind orders, or was a defined, protocols-based evaluation process implemented first?
The known United States history in the cold war with regards to assassinations targeted communist functionaries in disputed or contested regions. Not heads of state. When heads of states were targeted(Fidel Castro was a public example), they weren't successful.
I know Gerold Ford Feb 18, 1976, signed executive Order 11905 prohibiting employees of the United States Government from engaging in or conspiring to engage in all political assassinations. This was a response to The U.S. Senate Select Committee chaired by Senator Frank Church (the Church Committee) report in 1975 that found "concrete evidence of at least eight plots involving the CIA to assassinate Fidel Castro" from 1960 to 1965. Castro of course died in Nov 2016.
Cold War CIA assassination operations.
Operation PBFORTUNE - signed by Truman in 1952 authorized 58 names to be assassinated associated with Jacobo Árbenz the elected President of Guatemala. all 58 names were redacted when the CIA released their documents on the program. Although Jacobo Árbenz remained in office when Truman left office.
Operation PBSUCCESS, authorized by President Eisenhower in August 1953, carried a $2.7 million budget for "psychological warfare and political action" again against the President Jacobo Árbenz government of Guatemala. President Árbenz resigned from office in June 27, 1954, and died Jan 27, 1971.
The Phoenix Program ( 1965-1972 ) was said to be responsible for the deaths of 26,000 to 41,000 suspected NLF (National Liberation Front) operatives, informants and supporters during the Vietnam Conflict.
So to answer your question, what would have gotten someone on a hit list during the cold war. Living in a destabilized contested country and any aiding or abetting to the folks destabilizing would have been enough to get one on a hit list for the Phoenix Program. In Guatemala being a mid level functionary to the government of President Árbenz.