Probably not. The amount deducted from your paycheck was only your portion of the monthly premium cost. You do not need that information to file your tax return.
If you have employer-based health insurance, you may have received a 1095-C or 1095-B - neither of those documents get entered on your return. Only the 1095-A gets entered, and only Obamacare/Marketplace policies will generate a 1095-A tax form.
If you have a 1095-B, a form titled Health Coverage, the IRS does not need any details from this form. You can keep any 1095-B forms you get from your health insurance company or the government agency that sponsors your plan for your records.
If you have a 1095-C, a form titled Employer-Provided Health Insurance Offer and Coverage, the IRS does not need any details from this form. You can keep any 1095-C forms you get from your employer for your records.
Your state may request additional details.