Although the occurrence of road accidents and the number of road accident casualties in almost all Polish voivodeships has decreased over the last few years, the rate of this change varies considerably from region to region. To provide a better understanding of such a tendency, panel data regression models are proposed to conduct this pilot research which evaluates the relative performance of Polish regions in terms of their road traffic safety. Panel data are multi-dimensional data which involve measurements over time. In the research, a voivodeship is a unit analysed at a group level, whereas a year is a unit analysed at a time level. A two-way error component regression model has been applied to survey the impact of regressors, the group effects, and time effects on a dependent variable. The analysis has been conducted using data acquired from the Statistics Poland Local Data Bank website, as well as from the General Directorate for National Roads and Motorways. The panel data from 16 regions in Poland and the 2012–2018 period have been investigated. The examined models refer to road traffic safety indices defined based on the following characteristics: the number of road accidents, the number road fatalities, and the number of people injured. The results of all the three models indicate a negative effect as regards the GDP per capita, (car) motorisation rate, the indicator of government expenditure for current maintenance of national roads, and the road length per capita. A positive association has been found between the truck motorisation rate and the indicator of local government expenditure on roads. The impact of the region’s urbanisation indicators on road safety is ambiguous as, on the one hand, its increase causes a reduction in the road accident and accident injury indices, but, on the other hand, it produces a rise in the accident fatality index. In the models, the significance of time effects has been identified; a decreasing time trend suggests a general improvement in road safety from year to year. Most of the group effects have turned out to be highly significant. However, the effects differ as regards both the road accident and the accident injury indices in magnitude and direction.