The system regarding the use of conjunctive is the same independent of the fact that the phrase in question might be a question. If the question has an interrogative pronoun (see chapter 28) then the interrogative pronoun is used also in the subordinate clause of the reported speech. Is there no interrogative pronoun the subordinate clause starts with the conjunction ob. Actually the system is similar to the English as you can see in the following examples.

Some examples   She asks: "Why did he not come?" She asked why he did not come? Sie fragt: "Warum ist er nicht gekommen?" Sie fragt, warum er nicht gekommen sei. We asked: "What do you do there?" We asked, what did you do there?   Wir fragten: "Was machst du da?" Wir fragten ihn, was er dort mache. She asked me: "Do you have money?" She asked me whether I had money.   Sie fragt mich: "Hast Du Geld?" Sie fragte mich, ob ich Geld hätte. She asked me: "Do you go to the movies?" She asked me whether I went to the movies   Sie fragte mich: "Gehst du ins Kino?" Sie fragte mich, ob ich ins Kino gehe.