捕まる and 捕まえる: being caught and doing the catching
Separate the caught party from the catcher, comparing insects, arrest, and finding a busy person available.
The catcher and the caught party
犯人が警察に捕まりました。 says that the offender was caught by the police. With 捕まる, read つかまる, the caught person is the subject and に marks the catcher.
警察が犯人を捕まえました。 says that the police caught the offender. With 捕まえる, read つかまえる, the police are the subject and the offender is marked with を.
Catching an insect
子どもが網で虫を捕まえました。 says that a child caught an insect with a net. 網で marks the tool; 捕まえる is not restricted to arresting people.
捕まえた虫を観察してから、外に逃がしました。 says that the caught insect was observed and then released outside. 捕まえた modifies 虫 with the completed catching event.
Finding a busy person available
担当者が忙しくて、なかなか捕まりません。 says that the busy person in charge is hard to catch for a conversation or contact. It does not describe trying to arrest them.
捕まる becomes 捕まって, while 捕まえる becomes 捕まえて. Learn the forms with the different viewpoints of 人が捕まる and 人を捕まえる.
Who is caught, and who does the catching, in 犯人が警察に捕まりました?
Show the answer and why
The offender is caught, and the police do the catching. 犯人が is the subject but is the affected party; 警察に identifies the catcher.