You can easily set the collision polygon for a tilemap object.
Excerpt from the manual -
"When testing for collisions with a Tilemap object, empty (erased) tiles count as not colliding, and all other tiles count as colliding. A custom collision polygon can be set for individual tiles by clicking the 'Edit tile collision polygon' button in the Tilemap bar, or just double-clicking the tile in the Tilemap bar. Note however the collision polygon cannot be entirely removed from a tile: only an erased tile counts as not colliding at all.
If you wish to have tiles that are visible but do not register a collision, use two Tilemap objects layered on top of each other. Test for collisions with just the top object, and erase any tiles that should not register a collision. These tiles can then be placed on the tilemap object beneath, so they appear in the same place but are not tested for collisions."
When you have set the collision polygon for the tilemap, check the collision polygon for the character as well, as C2 likes to estimate it on import. Squares really work the best, if you don't need per pixel collisions.
If you need more help, you can post your capx and we can take a look at where things are going awry.