Most countries do it by subordinating secret agencies to a military division of sorts, wherein martial courts and security access is already structural. Others choose a more 'civilian' approach subordinated to a parallel chain of command within the citizen government/legislation/judiciary — closer to police, interior dpt / homeland security, etc. (in such cases, army intelligence is usually quite distinct from civilian surveillance).
Which approach is favored historically by a country typically depends on pre-existing constitutional models and principles — notably how the army features relatively to the ultimate civilian chain of command, and how the latter is accountable to the (sovereign) public in the event of treason.
None of this applies in authoritarian regimes where the ruling caste or figure(s) usually answer to no principle (no courts for them, only 'advisors' for they sit above the law) and secret service is almost always directly answering to them, as part of the active coercion of the people (fear of the "enemy within", etc).