It's a short way to say: ALthough HE (the policeman) WAS a little suspicious this time, the policeman gave him the same answer.

The dictionary definition is "despite the fact" The policeman was a little suspicious despite the fact that he believed the other person was possibly asking the same question again for ulterior motives. If we had more context we could be more specific with the answers.

"suspicious" is an adjective that modifies "policeman" "little" is an ADVERB that modifies "suspicious". "Little" is more often used as an adjective but also can be an adverb, as it is in this case: Question: How suspicious was the policeman? Answer: He was only a little suspicious.

"Suspicious" = not trusting something/someone, or a feeling like something/someone is not trustworthy. "Though," in your sentence, means something like, "regardless," or, "despite." Together, "though a little suspicious," means roughly, "regardless of not trusting things."