Should the subjunctive be used after the verb "asegurar que"?
The sentence I am trying to write is "La policía no se aseguraron que el niño tuviera un arma autentico o que él fuera una amenaza."
Is the use of the subjunctive tense correct here?
Yes, it is correct, the subjunctive is the correct verbal time that you need to use there, as both actions were ocurring in the past but at the same time or shortly after. Here, some uses of the "preterito imperfecto de subjuntivo" form are explained: http://espanol.lingolia.com/es/gramatica/tiempos-subjuntivo/preterito-imperfecto (I think this one is the first one)
It is in spanish, but I think you should be able to understand it, given that you're studying the more complex conjugations.
Also, let me rewrite the sentence for you, and correct a couple other mistakes which you might want to edit.
"Policía" is also used as a collective noun, so you should use a singular form for the subjunctive. Being a past tense, you should write it as "aseguró". The complete phrase would be:
"Arma" is a female noun for weapon and that's the reason why "auténtica" is the correct form of the adjective in this case.