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 that on February 18, 1976, President Gerald Ford 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.
The CIA has long been happy to kill operatives and functionaries, but with the notable exception of Fidel Castro, it has refrained from performing political assassinations, in favor of allowing local proxies and interests to do so. This provides political cover in the form of plausible deniability, especially when the Agency designs its signals of approval to be ambiguous, as it apparently did in the case of a coup planned against Ngo Dinh Diem.
The Chilean example is illustrative of the degree to which the CIA kept its hands off of political assassinations. Operation Condor, an arrangement in which right-wing South American governments received CIA backing and training, empowered them to target their own political enemies. In Chile, not only did the CIA-backed coup of 1973 cause the violent deaths of President Salvador Allende and folk singer Victor Jara, Pinochet's spymaster Contreras proceeded to arrange attempts on the lives of General Carlos Prats (1974, successful, in Buenos Aires), ex-Minister Bernardo Leighton (1975, unsuccessful, in Rome), and ex-Ambassador Orlando Letelier (1976, successful, in Washington, DC). The fact that the assassination program of an intelligence operation directly supported by the CIA had achieved its deadly goal inside the United States caused a scandal. The CIA was directly implicated, and had some foreknowledge of the plot, but did not prevent it. As the crime happened in the U.S., the Federal Bureau of Investigations worked to solve the case. This pitted two branches of the U.S. government against each other in an embarrassing fashion that the CIA would have sought to avoid in its own operations.