It depends on whether the adjuster works for the other driver's insurance company or yours. If the adjuster is from the other driver's insurance company, you are not required to talk, and you should not give him or her any information. Tell the adjuster to contact your lawyer. Do not give details about the accident or your injuries. You can be sure the adjuster wants to get information to use against you and that will hurt your claim.
Your obligation to your own insurance company is stated in your policy. Most policies require you to cooperate with the insurance company's investigation of the accident. But since even your own adjuster sometimes wants to get information to lower the value of your claim, you should consult your lawyer before giving a statement.