Why is there tar leaking into the attic

All the advice so far about ice damns is valid. However, if there are no dams or visible water on the roof, then you will need to crawl up in the attic and start looking for the wet areas that are wicking into your ceiling. The insulation may have been soaked before you got a chance to clear the roof. Obviously if wet insulation is found, it must be removed. Another problem I have come across in a few situations like yours, no dam, but slow moisture stains keep developing, came from improperly installed "proper vent" from the soffit vents to the air space in the attic. In a few cases, the open upper end of the proper vent was blocked or covered with insulation and condensation formed on the top side of the drywall right along the wall. In a couple of cases, no venting was used from the soffit and insulation was packed into this area instead. In either case, you will have to get up there and move the insulation in the affected areas and look for the moisture. Also look for any tell-tale water stains on the rafters or trusses that may have been a leak from above.

I have had several calls since Irene for similar problems on roofs that had previously had no leaks. As most have already said, the first step is to get up in the attic for a visual inspection. I would remove the insulation over the stained area to check for damp insulation and allow the ceiling drywall to dry completely. Look straight up over the stain area on rafters or trussed for any signs of water staining. You may get lucky and be able to trace a stain trail to the source of the leak. It is not uncommon that in a storm with wind driven rain for water to be forced uphill into a ridge vent, then track down a framing member. If this is the case, it was an isolated incident and no repair may be needed. However if the winds lifted a few shingles or damaged the seals around vent pipes etc., some simple repairs may solve the problem.

A word of caution, if you call in a professional roofer, get more than one opinion. It is very common in that trade to try to up sell uninformed home owners on a whole new roof at around $350 per 100 sq foot, rather than just offer a simple inexpensive repair. I would try to find a reputable general contractor in your area that will work with you as you learn more about home ownership and give you expert advise and recommend reputable tradesmen for roofing, plumbing, electrical etc., as needed. The best way to find such a resource is by referral from other homeowners or friends. Rarely will a really good GC advertise, as they are too busy already and get plenty of work from referrals from their customer base. Sometimes you can chat with a project pro at a local building materials center, even a Home Depot or Lowes and they may give up the names of a couple of good, well respected home maintenance general contractors.