I don't think so. Where do you live? It's a bit early for crabgrass in most of the northern half of the country.

Looks like Orchardgrass to me.

I believe it's a paspalum, specifically dallisgrass. The image given by UGA in the link is during summer when it's fully mature. It's very recognizable when it produces the seed heads seen in one picture.

Unfortunately, MSMA was taken off of the residential market, so killing it is a bigger challenge these days. If you don't have much in the lawn, I recommend digging it out. Dallisgrass is much easier to pull up than most perennial grasses.

Here is a link that might be useful: dallisgrass from uga.edu

It is Dallisgrass, 100% sure.