Not the Military Police.

The Guardia Civil, the takedown petitioner, is one of the two Spanish national police forces, the Military Police is a different corps entirely which belongs to the Army.

The Guardia Civil is similar to the Gendarmerie corps from many countries, such as France. However it does follow a military-style rank structure, which nothing out of this world for a police force.

Both Guardia Civil and Gendarmerie are part of the Army (but take orders from a civilian hierarchy) and are strictly speaking military police. But they don't police the military, which is what you probably had in mind.

Well, first and foremost they are not the Military Police. The OP seems to use that terminology for a hyperbolic effect, I find this attitude very frustrating giving the sensitive aspect of the situation in Catalonia.

Secondly, they are not part of the Army, they are self-described as a "full bodied police force" [1] and they report directly to the Ministry of Interior and only report to Defense in case they take part in a armed forces mission (article 9b of this law: [2]), which is seldom the case.

Like I said they do have a military-style rank structure, which they describe as for "efficiency for performing our duties" or "military nature" [1] as they were created as an infantry division back two centuries ago.

[1] http://www.guardiacivil.es/en/institucional/Conocenos/idcorp...

[2] http://noticias.juridicas.com/base_datos/Admin/lo2-1986.t2.h...