Which thing do you want to build? If it is the pergola or the deck and it is attached to your house, you would need a building permit. If the pergola is not attached to the house, you should be OK. If it were a free standing deck (not attached to the house), it may go either way depending on your community and how the building commissioner views it.

The best thing to do is go to your town hall and ask in the building department.

Well It wouldnt be attached to the house but my husband does want to attach it to the ground in some way, maybe dig the posts in.
what we want to build is just a deck similar to the one in the picture, not exactly the same, basically the bottome with 4 posts the the slats going across the top, with some latice on the street side.

Check with your building department. Sometimes these have to also meet zoning setbacks or even lot coverage. This is the wrong place to get an answer. You have to go to your building department.

check with the building dept. around here you have to get a permit for anything over 120 sq ft, especially if it is secured in the ground.

also, don't forget to CALL BEFORE YOU DIG! it is the law in all 50 states.