The short answer

None of the variables in a regression or path model (i.e., when all variables are manifest/observed), none of the parameters are constrained to equality by default.

An example with explanation

Below is a simple two-group path model with an observed variable y regressed on three other observed variables, x1, x2, and x3.

    Data:
      File is D:datamydata.dat ;
    Variable:
      Names are female x3 x1 y x2;
        Missing are all (-9999) ;
      grouping is female (0 = male 1 = female);
    Analysis:
      Type = general ;
    Model:
        y on x1 x2 x3;

We have omitted most of the Mplus output file.  To download the entire file click here. Below is the MODEL RESULTS section for males and females (the output for males appears first, followed by the output for females). Comparing the regression coefficients (denoted ON), the intercept and the residual variances, we see that none of these coefficients are constrained to equality by default.

MODEL RESULTS

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

Group MALE

 Y        ON
    X1                 0.352      0.105      3.365      0.001
    X2                 0.050      0.089      0.560      0.575
    X3                 0.450      0.105      4.307      0.000

 Intercepts
    Y                  8.205      4.798      1.710      0.087

 Residual Variances
    Y                 55.518      8.231      6.745      0.000


Group FEMALE

 Y        ON
    X1                 0.453      0.102      4.455      0.000
    X2                 0.046      0.084      0.546      0.585
    X3                 0.211      0.098      2.161      0.031

 Intercepts
    Y                 13.632      3.958      3.444      0.001

 Residual Variances
    Y                 43.290      5.864      7.382      0.000