An attorney can respond to discovery if the responses are nothing more than objections. Otherwise, the responses need to be made by a person with knowledge of the information who can verify those responses.
If you are involved in litigation then ask your attorney who is defending you and dealing with opposing counsel on such matters. Whatever concerns you have are best presented to your lawyer.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.
I agree with the previous answers. Unless the response contains only objections, it is improper for an attorney alone to sign discovery responses.
Also keep in mind that in California, a corporation cannot usually prosecute an action in Superior Court without being represented by an attorney. Make sure if you are a corporation involved in a lawsuit in California that you are represented by an attorney.