We advise all of our clients to speak with their own insurance company only to notify them of a claim. You should not be speaking to the opposing party’s insurance company at all before you have hired an attorney.
You have a responsibility to inform your insurance company that you have been in an accident. However, the best case scenario is to not speak to them at all, and hire an attorney as soon as possible to represent you in your claim, and notify the insurance company for you.
If you do notify them of your claim, simply provide them with basic information such as the date, time, and location of your accident. That is all they need to be on notice of your claim. Any additional information they are requesting, such as your take on who was at fault, an assessment of your injuries, and whether there are any witnesses will be information that your attorney will provide to them.
Remember that while you have paid your insurance company, their main goal in this process is to not pay out any claims. In the event that you have to file an uninsured or underinsured motorist claim, you do not want to give any information that could hurt your claim in the future.