Is a good practice to sum each rate (i.e. crime rate per 100.000 people)?
This can be fairly good if you deal with few years.

In general it's not a good practice, since asymptotically will lead you to have almost the same fraction of crimes per all the considered years. But unless you have data from the last 10000 years, you can simply ignore the asymptotic behavior a continue the way you are doing.

Otherwise, you can normalize the data to a reference value, say the maximum number of crimes on the series. This is more robust.