Perhaps contrary to common belief, there are (actually lots) of competitive & relatively free elections held in China, especially in the 2007-2012 reform era. However, those were limited to the local level, and the elected officials had little influence at higher levels.
Competitive and relatively free elections are held at the village level. Under Chinese law (Articles 30 and 111 of the PRC constitution), villages do not constitute administrative units (i.e., there is no "village-level government"), and are instead "organs of local autonomy".
Every village has a Villager's Committee, and members serve terms of 5 years. Those elections are relatively free, in that every villager over the age of 18 can run, and there's no pre-approved list of candidates. Committee members have vast powers over the administration of the village, and has some oversight over the policies of the local township government. However, there are lots of problems with this system: corruption & nepotism is an apparent one, and elected officials are often subject to pressure from the local township and/or county government.
The elections for local People's Congresses, i.e., legislature, remain under tight control. The elections are competitive, but all the candidates are pre-approved by local government and party organs. Very occasionally, non-pre-approved candidates somehow make it into the list of candidates, but those candidates are often pressured, sometimes violently.