(CNN)In counties where states require masks, Covid-19 case and death rates slow down -- but in counties where states allow on-site restaurant dining, illness and death rates appear to speed up, according to a new study from the US Centers for Disease Control and Prevention.

The research, published by the CDC on Friday, comes at a time when several states are expanding business capacity and lifting or preparing to lift mandates for people to wear masks -- with Texas and Mississippi joining those states this week.

The new study takes a close look at changes in the growth rates of Covid-19 cases and deaths in counties before and after state-issued mask mandates were implemented and restaurant dining was allowed from March through December of last year.

The researchers found that, from March 1 to December 31, requiring people to wear a mask outside their home or in retail businesses and restaurants was tied to a 0.5 percentage point decrease in the daily growth rate of Covid-19 cases up to 20 days after the mask mandate was implemented. Decreases up to 1.8 percentage points were seen up to 100 days later.

Mask mandates were associated with a 0.7 percentage point decrease in daily rates of Covid-19 deaths up to 20 days after implementation and decreases of up to 1.9 percentage points up to 100 days later, respectively, the researchers found.

For restaurant dining, changes in daily growth rates for Covid-19 cases and deaths were not statistically significant up to 40 days after restrictions were lifted, according to the study.

But allowing on-premises restaurant dining was associated with 0.9, 1.2 and 1.1 percentage point increases in cases up to 60, 80 and 100 days, respectively, after restrictions were lifted, the researchers found. Allowing on-premises dining was associated with 2.2 and 3 percentage point increases in the Covid-19 death growth rate 61 to 80 and 81 to 100 days, respectively, after restrictions were lifted.

The study did not control for other Covid-19 safety measures in counties and states that could have influenced the data, and the analysis did not differentiate between indoor and outdoor dining.

"Mask mandates and restricting any on-premises dining at restaurants can help limit community transmission of COVID-19 and reduce case and death growth rates," researchers from the CDC and University of Nevada wrote in the paper. "These findings can inform public policies to reduce community spread of COVID-19."