Hire a PM company but still personally screen tenants?

[Eric C.]

Is there any way to have a property management company handle the midnight calls, the routine maintenance, the drama, the toilets, the yard, and everything like that... but personally handle the tenant screening and application process/documentation?
The reason is because I feel I can do a good job of tenant screening and organized documentation of everything. Not only that I [i]prefer to pick the tenants and make sure we're A OKAY on legal everything to avoid discrimination suits.