Unless you have a court order stating that you must pay for his health and auto insurance, then you are not obligated to do so. However, if you or your husband file for divorce or separation, it is normal for a court to prevent either of you from making any changes to things like insurance or finances. From the facts you stated here, though, you have potential liability for paying spousal support. I would recommend you speak to an attorney as soon as possible to protect your interests. Good luck.
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Let me add to what Jennifer said. Most courts do make orders once the divorce is filed not to do this. But, it's more than that. There is a statute prohibiting it. http://codes.ohio.gov/orc/3105.71
Read section A closely and it says not to do it if you do so immediately preceding the file of a divorce. The cost to you doing so could be astronomical. My suggestion is keep the insurance in force. It's not worth the risk.
See this as well for a good summary. http://www.cornwell-law.com/01/columbus-ohio-divorce-lawyer-on-divorce-in-ohio-part-7/
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I would also caution you that while you may be legally able to terminate the health and automobile insurance you provide for your spouse before a divorce action is filed, you may also be held responsible for any debts incurred by your spouse which result from the termination of coverage by a domestic relations court. It is almost always a better decision to maintain insurance coverage until the marriage is terminated.
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