Learn Polish: Policja szuka zabójcy. - The police are looking for the killer.

In Polish, policja is a singular feminine noun. Even though it represents a collective group of people, it grammatically takes a singular verb, much like the English word "family". You would only use the plural if you were talking about the police forces of several different countries.

Why is the word for "killer" in the Genitive case (zabójcy) instead of the Accusative?

The verb szukać (to look for) is one of several common Polish verbs that always demand the Genitive case for their direct object, even in affirmative sentences. Other common verbs that do this include słuchać (to listen to) and używać (to use).

The dictionary form is zabójca, which ends in "-a". Does that make it a feminine noun?

No, zabójca is a masculine personal noun. However, because it ends in "-a", it follows the feminine declension pattern in the singular. That is why its Genitive form is zabójcy (just like the feminine noun praca becomes pracy). Keep in mind that any adjectives describing him would still be masculine, for example, groźnego zabójcy (of a dangerous killer).

Could I use mordercy instead of zabójcy here?