Eyewitnesses say the students were bundled into police cars after clashes in the town of Iguala on 26 September.
They have been missing ever since and forensic tests carried out on bodies found in nearby mass graves indicate they are not those of the students.
Thirty-six municipal officers are being questioned over their disappearance.
National Security Commissioner Monte Alejandro Rubido said that during the investigation into the students' disappearance, the authorities had found "irregularities" and "presumed links to organised crimes" in 12 municipal police forces in Guerrero state and one in neighbouring Mexico state.
Among the towns to which the federal police have been deployed are the popular tourist destinations of Taxco, famous for its silversmiths, and the spa town of Ixtapan de la Sal.
Mr Rubido said municipal officers in the 13 locations would be interviewed and their performances reviewed. Their weapons have been confiscated.
The move comes after officers from the town of Iguala reportedly confessed to handing the students over to a criminal gang called Guerreros Unidos (United Warriors).
The 43 missing students all attended a teacher training college in Ayotzinapa with a history of left-wing activism, but it is not clear if they were targeted because of their politics.
Some locals say they may have angered the gang by not paying it protection money.
Police also want to question Iguala's mayor, his wife and the police chief, all of whom are on the run from the authorities following the events of 26 September.
Drug gangs in Mexico often infiltrate local government and security forces to ensure they are not disturbed in their criminal enterprises.
Poorly paid and badly trained municipal police officers are an easy target for criminals offering bribes or threatening reprisal attacks on those who refuse to collaborate.
Meanwhile, the search for the missing students continues with teams of dogs combing the countryside and checking abandoned mine shafts, caves and wells.
Forensic tests are also still underway on bodies found in a number of mass graves in the surrounding area.
Twenty-eight bodies found on 4 October have been tested so far, but more than a dozen other burial pits have been found since.
Mexican federal police have taken control of 12 towns in Guerrero state, where 43 students disappeared after clashing with the municipal police.