I find it unlikely that life was seeded on Earth with "cross-contamination" from Mars in the form of an impactor or Martians zooming over to Earth and pouring some goo in the water.
Note that I said unlikely. It is not impossible nor is it absolutely certain without further proofs. Therefore, it is either likely or unlikely to varying degress. In this case, and especially because we do not know that there was ever life ON Mars, it is more unlikely as opposed to less unlikely. When or if we FIND evidence of past life on Mars, then it may or may not be more likely.
That said, considering that we've discovered organic compounds in space (including ethanol!), how is it unlikely that life on Earth started on Earth? Not very. Why? Because we KNOW there are organic compounds floating around in space and that they might find their way to any planet where further synthesis leads to RNA, then DNA, and life.
Those organic compounds would likely have been present in great quantity in the early Solar System and sucked up by forming planets as they accreted. If Venus were "habitable" in the Early Solar System. perhaps life started there as well. The same with Mars and Earth.
One could make the argument that Mars, due to its lower mass and greater distance from the Sun would have cooled before Earth and therefore had life before Earth, but that's speculation. Before we can even entertain the idea of Martian Life somehow seeding Earth, we have to prove there WAS (or is) life on Mars to begin with. That. we have not (obviously) done yet.