We decided to put dash cameras in the vehicles of people who have had several accidents to see if there might be a problem with their driving.
この場合、次のような言い方ができますよ。
ーWe decided to put dash cameras in the vehicles of people who have had several accidents to see if there might be a problem with their driving.
「事故を何度も起こしたことがある人の車にドライブレコーダーを取り付け、運転に問題がないか確認することにした」
to put dash cameras in one's vehicle で「車にドライブレコーダーを搭載する・取り付ける」
ご参考まで!