There is some guideline for reporting crossover clinical trials?. I am not sure, but I think there is not any extension of CONSORT to report crossover clinical trials.
Didn't find much, but this might be a place to start. See the article in Trials: Design, analysis, and presentation of crossover trials. In particular, the references in this article could be of more help than the article itself. See link below.
It refers to understand human experiments such as those performed to assess efficacy and safety of drugs. The full name is the Clinical Trial Double Blind Controlled Azar, where an intervention compared (such as drug treatment) vs placebo intervention or no intervention (like the drug but without pharmacological effect).
For the results to be valid and reliable, it has to perform double-blind design (in case of drug research, neither the patient nor the researcher or physician must know who receives medication and who placebo)
The validity of the results is greater when not only experimental group vs placebo group, but is double-blind, crossover and also compared. Ie, a drug begins with group and the other with placebo, after a set time, exchange treatment.
This double-blind crossover design is called factorial.
The data obtained can be described and analyzed using parametric or non-parametric statistics depending on the type of variables. Data as two groups (experimental vs control) in 2 or more situations are compared must be analyzed with variance of one or two lanes (parametric "ANOVA" or nonparametric "Friedman, Kruskall Wallis").
There are pre-programmed commercial packages (software) such as SPSS, STATA, EPISTAT and Excel Plus, which are very useful.
For the structure and wording of writing to publish, follow the guidelines of the International Committee of Biomedical Journal Editors.
The crossover design to study the differences in treatments yields a more efficient comparison of treatments than a parallel design. Subjects are on their own controls. The within-patient variation is less than between-patient variation. Crossover design requires a smaller sample size than a parallel design, but achieves same level of statistical power. However, there might be a potential carryover effect in crossover design. A washout period should be long enough to minimize the carryover effects and precision. In clinical trial studies, the length of the washout period usually is determined as some multiple of the half-life (t1/2) of the study medicine within the population of interest. Generally, a washout is at least 5 times of the t/12.
crossover designs are used in many phases of clinical development; for new investigational products and, more often, for generic drug testing. Below are two links of FDA guidances on bioequivalence and bioavailability studies. The guidelines are not about crossover design but some parts are dedicated to designs and issues around these designs (as Govani has mentioned eg. washout period). In crossover design, typically the treatments are switched 4 times to ensure consistency of the effect.
Other jurisdictions (FDA is in US) may have similar legislation/guidelines for generic and non-generic drugs.
I am not aware about any guidelines which specifically deal with crossoverreporting with exceptions of overall requirement for clinical trials reporting.