I have a small full bathroom. On the backside of the bathroom is a large walk in closet that I am converting into a laundrey room. Is it possible to put t's in the supply line to the shower to also feed the washer and what is the best way to tie in my drain?

Its OK to tee the supply lines but no tees on a drain. You give us no info on your drin pipes so its hard to say about connection. Is there a basement or crawl under this area?

Washing machine is better not being put in wet area.

tingsfly the laundrey will share a common wall with the bathroom but be in a separate room...
Ballengerb... the waste line runs through the wall in the bathroom ajjacent to where I will be putting the washer machine... the vent extends through that wall as well... I do not have access to below as it is a condominium unit

Do you have a Home Owners Association?

Yes

Have you checked with the association about thud? Their could be a common property issue here