Although you may refuse to answer questions during a deposition in a civil proceeding your failure to do so may have consequences in that action. This question raises serious issues involving your Fifth Amendment rights. You should retain experienced counsel to assist you with the civil and criminal matters that you appear to be involved in.
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I can't tell from your question if you are a victim or a suspect. Either way, you need a lawyer. There is too much at stake to do this without professional help.
This answer is for general education purposes only. It does not create an attorney-client relationship nor is it intended to provide legal advice. The answer is based on the limited information provided and the answer might be different had additional information been provided. You should consult an attorney.
If you are accused of rape and the case is in the criminal courts, you should hire an attorney or ask the court to provide one. If you are being sued in civil court for the damages from the alleged rape, you should hire an attorney. The 5th Amendment protects you against self incrimination. However, you can waive that right and it will be used against you. In other words, you can end up in jail if your words are used against you.