you can achieve this affect in After effects if you have that. The quickest and easiest way to do this with buying an extra plugin is to use photoshop to create a single layer picture of your blood drip as you want it to appear at the start of your animation. save it as a psd and go to after effects. In after effects create your composition to your chosen aspect ratio. import your blood pic. use the liquify effect that comes with AE 6.5 (i assumed that was what you'd be using) to "drip" the pic down to the bottom of the screen (or wherever you want it to stop) using the key frames from the begining to the end can crete a quit convincing blood effect.
A better Idea, though, is to go oldskool on the effect. Take your camera and set it on a tripod facing a blue/green screen. attach a matte box to your camera lense (if you don't have a matte box the spray paint a cardboard box black on the inside, cut out one end.) Insert or attach a clear glass or plexiglass panel at the open end of the box (facing the blue screen). make sure the blue screen is lit well and evenly. light the glass panel so as to avoid glare but supply bright light (i recommend lighting it from the bottom for color reasons {blood is darker at its source}). When all is set and lit, squeeze fake blood or well mixedfood colored red milk from a sponge onto the glass. try it a couple times to get your effect.
If you do it the old skool way, use Premier's blue screen keying effect to remove the blue/green screen and leave only the blood drip.
A bit long explanation, but at least it's informative.