I'd like to install a utility sink in the basement and have attached a drawing illustrating the current piping and proposed attachment.
Basically, the kitchen sink drain goes directly into a drain in the basement floor via a 1-1/2" steel pipe, which is tied to the sewer system. I'd like to put a tee (y) joint in the steel pipe and connect to the utility sink.

Thanks
Djh in Central Pa, usa

Yes, it looks fine. Don't forget to install vent.

First increase to 2" and replace the 90's with sweeps and lose the dogleg, 45 over instead.
As Milo pointed out you will have to vent the new sink. This can be done by running a pipe out the roof or a AAV,( Air Admittance Vent) as shown.
Good luck, Tom