Is it illegal to pretend to have a Service Animal?

Yes, it is a crime to pretend to have a service animal.

Some dog owners disguise their dogs as service animals in order to break laws regarding health and safety, and the practice is causing alarm among the truly disabled. Read Fake Service Dogs a Growing Problem as Pet Owners Flout Disability Rules.

The law makes it a crime, with a penalty of up to six months in jail or a $1,000 fine, to pretend to own or train a guide, signal or service dog. See California Penal Code section 365.7:

365.7. (a) Any person who knowingly and fraudulently represents himself or herself, through verbal or written notice, to be the owner or trainer of any canine licensed as, to be qualified as, or identified as, a guide, signal, or service dog, as defined in subdivisions (d), (e), and (f) of Section 365.5 and paragraph (6) of subdivision (b) of Section 54.1 of the Civil Code, shall be guilty of a misdemeanor punishable by imprisonment in the county jail not exceeding six months, by a fine not exceeding one thousand dollars ($1,000), or by both that fine and imprisonment.

(b) As used in this section, "owner" means any person who owns a guide, signal, or service dog, or who is authorized by the owner to use the guide, signal, or service dog.

See more info at leginfo.legislature.gov.