No, you do not issue Form 1099s to the insurance companies for the premiums you pay for health, life or disability. There are not consider medical or health care payments since you are buying policy and paying premiums towards it. You are not paying for health care services.
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Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases.