We are not aware of any law that would prevent your 16 year old daughter from obtaining a car or insurance on it in New York at her age. There are some insurance companies though that will want her to have a full active license, so if she has only a permit or junior license then it may be harder for her to find insurance for a car.
If you purchased your daughter a car and put it in her name and wanted her to obtain her own insurance, this would usually cost more than if the car was insured by your household policy. Also since your daughter is sixteen the insurance company would require a parent or guardian to sign on the insurance contract/policy with her since she is a minor. Thus if you want her to get her own car insurance policy to get away from liability, you would normally still have some liability on you by signing on her insurance with her and because she is a minor living in your household.
If you have concerns about your daughter and your liability or policy limits, you may want to consider obtaining an umbrella policy that would help to protect your assets.
Free Auto Insurance Quotes
[Let CarInsurance.com help you find affordable auto insurance now.] We have recently partnered with Safeco to offer umbrella policies which you can get to by clicking on this link or calling 1-800-936-0356.Safeco's Personal Umbrella policies are competitively priced and offer exceptional coverage. You can receive coverage up to $2 million.
Umbrella policies are available to Safeco customers who insure their personal autos with Safeco. You may have to have certain liability limits in order to qualify for Umbrella insurance (availability is subject to state laws, compliance and underwriting). | 
