If I withdrew money from an annuity due to COVID/reduced work hours, will I still be taxed an extra 10% on top of federal and state income tax?

No, you will not have to pay a 10% penalty.  Withdrawals from a IRA because you were affected by COVID-19 are not subject to the 10% early withdrawal penalty.  Additionally, the tax on the distribution can be paid over a three year period. You’ll have that time to pay back the funds you withdrew, without the amount impacting that year’s cap on contributions, and if you pay back the amount within that time, you’ll be able to claim a refund on those taxes.  

In order to waive the penalty and elect to the option to pay the tax over three years, you will have to complete Form 8915-E.  At this point and time the Form 8915-E (Qualified 2020 Disaster Retirement Plan Distributions and Repayments (Use for Coronavirus-Related Distributions)) has not been finalized.

To sign up to be notified when this form is live, click on the following link:  

Why am I getting getting a 10% penalty on my 1099-R when I withdrew fund during Covid? (Form 8915-E)