Learn Danish: Politiet anholdt en mand i forbindelse med sagen. - The police arrested a man in connection with the case.

Unlike in English where "police" generally takes a plural verb, in Danish politiet is singular. It is the definite form of the neuter noun et politi. If you needed to refer back to it with a pronoun later in the story, you would use det (it), not de (they).

Why is it anholdt and not anholdte?

Anholdt is the simple past tense of the verb at anholde (to arrest). It is a compound of holde (to hold), so it uses the same irregular past tense form (holdt). You would only add an "e" to make it anholdte if you were using it as an adjective to describe a definite or plural noun, like in the phrase den anholdte mand (the arrested man).

Is i forbindelse med a fixed expression?

Yes, i forbindelse med is a very common fixed phrase meaning "in connection with" or "in relation to." It is widely used in news, police reports, and formal Danish. You cannot swap out the prepositions; it always takes i at the beginning and med at the end.

Does sagen only refer to a police or legal "case"?

While it clearly means a criminal or legal case in this context, the root noun en sag is much broader. It can mean a matter, an issue, or a cause. For example, you will often hear en god sag meaning "a good cause," or det er din sag meaning "that is your business" or "that is your problem."