Towing Issues: Real or phony no parking signs?, homemade signs, construction crew

Question
I live in Los Angeles and in my neighborhood their is a major lack of parking
for the residents.  The other night I was looking for parking where I would not
have to wake up early to move my car and I saw that a construction company
working on a house hade taken over part of the road where I usually park.  
They put a mobile office on the street parking and had put yellow tape ad a
homemade no parking sign up to block off space so they would not have
trouble getting parking when the workers arrive in the morning.  Can the
construction crew just put up parking signs on public property like that?  If I
moved the sign and parked there, would they be able to find a tow truck that
would tow my car on public property?

Thanks for your help on this question.

Answer
Well I know that Construction and the related parking issues create many problems...  Unfortunatly I do not have specific answers for the Los Angeles area on this one as I was doing some research for this one and really can not find specific rules on the use of "homemade signs"..

Best answer I have would be to contact the police department parking division and see what they say... I did find that they can have areas marked so they can gain access to the site, but as far as the mobile office parked in the street, I did find some references to permits required and then also some references that they could not leave the office on the street... Kind of confusing to search all that stuff with the state laws also being referenced..

Check with the police as they would be the "KEY PEOPLE" involved who either ticket or permit it to happen.