There is a great Mountain Rescue in Poland, called GOPR ("Górskie Ochotnicze Pogotowie Ratunkowe" - "Mountain Volunteer Search and Rescue"). They cover all the mountain regions of Poland and in case of emergency you can reach them calling free rescue number: +48 601100300. There is even a smartphone app you can use to call help called "Ratunek" (https://play.google.com/store/apps/details?id=com.pagasolutions.emergencycall), which sends the rescue team your GPS coordinates; as far as I know it's only in Polish, though.
In Tatra mountains exists a separate, more specialised rescue organisation called TOPR ("Tatrzańskie Ochotnicze Pogotowie Ratunkowe" - "Tatra Volunteer Search and Rescue"). As Tatras are the only mountains in Poland with alpine character, the specificity of rescue services is different there, hence different rescue organisation. Emergency number 985 works in Tatra, but calling +48 601100300 will also work, as both organisations cooperate closely. TOPR also provides information about weather, condition of trails and avalanche danger on their webpage http://www.topr.pl/ (only in Polish, but you can always use google translate).
Rescue services are free in polish Tatras, in contrary to neighbouring Slovakian Tatras, where you need to pay search and rescue costs. However, you should consider getting good insurance for medical expenses, unless you are EU Citizen. As a last note I wanted to add that the quality of Mountain Rescue that TOPR provides is top-notch. Rescue officers are stationed in various mountain huts around Tatra, allowing for fast reaction times. There is also a rescue helicopter on duty in headquarters in Zakopane in case of more serious injuries. The standard you should expect is similar to that in the Alps. So don't hesitate and enjoy Polish mountains!