Does the filing of a criminal complaint trigger a defendant's right to a speedy trial?

Appellant's federal constitutional claim in the misdemeanor case requires a different analysis. "[W]hen an offense is charged as a misdemeanor it is the filing of the complaint (or earlier arrest) which triggers the defendant's Sixth Amendment right to a speedy trial." (Serna v. Superior Court (1985) 40 Cal.3d 239, 245 (Serna).) Here, the complaint was filed on March 3, 2009; appellant was arrested in March 2011; and appellant entered his plea on April 27, 2011, slightly less than two years and three months after the filing of the complaint.