What happens if you connect a capacitor in parallel with a current source depends on the rest of the circuit. The AC impedance of a current source is large (depending on the configuration) but the capacitor will pass the AC signals forming a high pass filter with the internal resistance (parasitic) of the current source. From a DC point of view if the rest of the circuit does not draw current the capacitor will charge linearily to the saturation voltage of the source.
When you connect a capacitor in series with a voltage source you block the DC current. However the AC current will pass and since the AC impedance of the voltage source is low AC current will flow to ground. What kind of configuration do you have in mind?