"used to" isn't an auxiliary, like BE or HAVE, so it cannot function like an auxiliary. It need DO-insertion like other verbs:
1. Did you use to work here? <See Note below, the -d on used is dropped and picked up by Did>
2. No, I didn't (use to work here). <See Note below, the -d on used is dropped and picked up by Did>
2. Max said (that) they used to work here.
Note,
When do occurs with used to in negative statements and in questions, use to (not used to) is correct: You did not use to play on that team. Didn’t she use to work for your company?
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